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"N$(A)crc|8W(N1):13:"Select Segment: "; d10W(N1):4:Eĺ"1-"N" or "M$"J"M1$" "M$"K"M1$" select; RET$):N$(A)"Return to Program":R$(A)"#":AA1:11PP11ebN$(N$,2):(N$,1)"0"(N$,1)"9"280ob"NA1b,W2:N7W1b61:" ______________________________________"b@Z1$"____________";::" Teacher's Menu ";::"__________"Z2$;cJV31190=a$2F0,201,251,176,6,201,225,144,2,233,32,76,240,253Qa54,$2F0:1002[aAA1ea240vaN$(A),R$(A)aP1(21.5((N$(A))3)2):P1PPP1a190a216,0:(222)42ĦaN$:N$""290a(N$,1)"#"2907bN$(N$,2):S(N` "Teacher Menu 2`d::(21):E`nN$(20),R$(20)j`x(64435)234(64448)234E1`B$(8):M$(27)(15):M1$(24)(14)`Z1$"|":Z2$Z1$:EZ1$M$"Z"M1$:Z2$M$"_"M1$`P12a(64435)234Ĺ49162,0:">PR#3":(17):       110aL279,198L18:N$#aV:+a`486ajW12BatL114Xa~L2020,191:N$`a:ha16saW12aL114a295L20,0:N$a:a0a1aI1(28672)1aIaA$:A$" "1260aaIa ::NUN T `d(21)`n1:0*`$7000:$7000^`(8181)0ĺ">BLOAD]BLOCK,A$AE00":$1FF4,$AE00f`3`">BLOAD^END FRAMES,A$7000"`6:`0::3`1`N$`W12`L110`0,L1818:N$`$:`.32`8W12aBL 5279,153:1:1:3::56950:P10:P20. ߱H65,25279,153:1:1:3::56950:P10:P20d ߱DD,1)"."(DN$,DL1DD,1)"1"į265DD9,30I޺(DN$,DL1DD,1):DD:bޒ0:177,32264,46:hޱy޲ TRIG TABLEޯ1:1:20,46ޯAA$:2:2:1:†޲ TRIG TABLE FROM CALC׆ޯ:1:20,46ޯAA$:2:2:1(ޯ:0:165,2C055580!ޭ(DN$)DF8DC0ı<ް56990:DN$"0"DN$""\!ޭDC1DN$"":DC0:DF0:NF0u&DN$DN$DA$:56950:Dް56990:DN$"":200,30:"error":uޱvޯ:DN$""56990υ}ޭNF1į180,30:"-"-~DL(DN$):DD1DL:263DD9,30:(DN$,DL10*ݯ178,95191,105:P1178:P295:56850Sݯ202,95215,105:P1202:P295:56850|ݯ226,95239,105:P1226:P295:56850ݯ178,75191,85:P1178:P275:56850̄ݯ202,75215,85:P1202:P275:56850ݯ226,75239,85:P1226:P275:56850 ޭDS1D0:56950:|ݰ55400:DN(DA$):DN56740,56750,56760,56770,56780,56790,56800,56810,56820:178,135191,145:P1178:P2135:56850ݯ178,115191,125:P1178:P2115:56850փݯ202,115215,125:P1202:P2115:56850ݯ226,115239,125:P1226:P2115:56850:NF0:DN$""3ܰ56990:DF1:DN$DN$".":56950:cݰ55400:226,55239,65:P1226:P255:DC1ız"ݭ(DN$,1)"."DF06ݭ(DN$)2DN$"0":NF0:DF0:56990:56950:;ݭDS1DN$(DN$,(DN$)2)"0"(DN$,(DN$)1,1)" " @DN$(DN$,(DN$)1):5699DDܭDR3DNHNDD(ܭDR4DNHNDDCNF0:DN0NF1:DNDNtܰ55250:DN(DN$):56990:DF0:DN(DN)DF1HNDN:NF1HNHNܰ56950:DR0:Ձܰ55400:202,135215,145:P1202:P2135:DF1DC0ıܭDC1DN$"":DC0:NF0ܭDN$"0"DC:DP1:56430:DP0:DS0:DR3:b۰55400:250,75263,85:P1250:P275:DP1:56430:DP0:DS0:DR4:Pܰ55400:250,135263,145:P1250:P2135nDC1:DR0HN(DN$):NF1HNHN:qܭDR0ı܀xDD(DN$):NF1DDDDܭDR1DNHNDDܭDR2DNHNS$۰55400:250,115263,125:P1250:P2115:DC1İ56990:NF1:DC0:DN$"0":56950:u?ۭDN$"0"İ56990:NF1:56950:AۭDS1(DN$,2)"00"DN$(DN$,(DN$)3)"-00":56990:56950:BDP1:56430:DP0:DS0:DR1:۰55400:250,55263,65:P1250:P255:A~ٰ56990:DN(DN$):DN(DN):55250:DN(DN$):DN(DN)DF1]~DN$(DN):56950:DC1:~\ڰ55400:202,55215,65:P1202:P255~zڰ56990:HN0:DR0:DS0:NF0:DF0:DN$"0":56950:ڰ55400:250,95263,105:P1250:P295:DP1:56430:DP0:DS0:DR2:} ٭DN$"0"DS1(DN$)1000ıE}DS1:(DN$)DF3DN$(DN$,3DF)k}٭(DN$,1)"."DN$(DN$,(DN$)1)}DN$DN$"E+00":56990:56950:}DN$(DN$,(DN$)2)(DN$,1)DA$:56990:56950:~ٰ55400:226,135239,145:P1226:P2135:DF0:NF1İ56900׭(DN$)8DN$(DN$,4)(DN$,4)&|رV|ع216,0:(222)69(222)133(222)53ijg|د::DP1ġ|ذ56900:DR0:NF0:DF0:DN$"":55050|hحP10įP1,P2P113,P210:P10|ر|د2:2:1::|ذ55400:178,55191,65:P1178:P255:DC1ı,1)"."DN$(DN$,7)H{DU0:DD1(DN$):(DN$,DD,1)"."DU(DN$)DDm{ׂDD:DU4DN$(DN$,(DN$)DU4)s{ױ{DU(DN$)1:DD1(DN$):(DN$,DD,1)"."DUDD1{ׂDD:DN$(((DN$,3))100)"E+":DU$(DU):DU10DU$"0"DU${DN$DN$DU$: |z׭DA$"="İ56400'z׭DA$"."İ56500Gz׭DA$(8)DA$(136)İ56600rz׭(DA$)0(DA$)48(DA$)176İ56700}z׫55100zDN$(DN):DS0:DD1(DN$):(DN$,DD,1)"E"DS1zׂDD:DS155280z׭DN9999999955270{׭(DN$)8DN$(DN$,8):(DN$0:DP0:3::P10:P20:DN$"":559301y ץ55300Wy<ׯDA$:DA$(27)DA$(155)55500ky>׭DA$""İ57050yA׭DA$"E"İ55550yF׭DA$"R"İ55700yP׭DA$"C"İ55900yZ׭DA$"+"İ56000yd׭DA$"-"İ56100yn׭DA$"X"DA$"*"İ56200yx׭DA$"/"İ56300K DRAWER X1.2xX1,Y1X2,Y2]xLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNsxRE12.1LN1012xœX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)x꜂REx%y֯:1:1:0:165,25279,153:1:1:DF0:NF0:DC.":::">RUN END":!w34300*w900RUN INSTRUCTIONS.A"9v AN$"2"S31:910MvAN$"3"34200v0::3:30:40,60:N$:"IS GOOFING OFF!!"v1::v TT16:RRTT10TT105:250RR,RR:RR::TT:1:800:1:34000v ENDw2:0,176:"One moment..oose what you":"wish to do next by pressing the":"key of your choice."u䄯20:0,80:"1. Rerun the entire program":"2. Rerun the equilibrium calculation"u"3. Play a game":"4. Stop"uAN$:AN$"4"AN$"1"34040"vAN$"1"į0,160:"One mom150,41:"30":150,53:"30":2:165,42:"|":165,55:"|"et.1:130,24:"23 N":118,63:"23 N"t8800:0:0,90279,191:2:0,90:" Forces a, b, and c acting on":"point P are in equilibrium."tτ900tЄ 34Huڄ2:0,30:" You may now ch"{"$s186,31:"B":186,71:"C"s0,90:" If dog c pulls 40 N due west,":"dog a pulls 23 N 30| north of east,":"and dog b pulls 23 N 30| south of":"east, point P will not move."s6:134,56146,56:152,56164,56:170,56182,56;t$1:e of":"the same magnitude, vector b is":"also 23 N."_r}234,39:"b":1:226,37:"b=23 N"hr瀫900qr耲 33yr򀯾2s1.5:50,52:"}":52,37:"A":74,41:"40 N":2:3:64,56124,56164,36:124,56164,76:123,39:"P":166,32:"{":166,72:66 =":130,124:"20 N":143,135:"a":129,139165,139q}79,158:"a =":130,151:"20 N":131,166:".866":128,166165,166:178,158:"= 23 N":158,39:"a":1:129,37:"a=23 N"6r}800:2:0:0,90279,191:0,90:" Since vectors a and b arate the lengths of vectors":"a and b by using the cosine":"function."p}2:162,69:"c'":229,69:"c'":800:0:0,90279,191p}2:30,100:"cos 30| =":128,93:"side adjacent":137,108:"hypotenuse":3:1:126,109231,1099q}54,129:".8s are":"equal, the vectors a and b are of":"equal magnitude and cross half way":"along vector c.":2:196,55:"c":2:198,70198,40:800:0o}}0,90279,191Gp}2:0,90:" We now have two right triangles":"with sides c' = 20 N. We can":"calcul51:"|":800:0:0,90279,191nn}2:0,90:" Since the sum of the interior":"angles of a triangle always is 180|,":"the other angle must be 120|":1:185,43:"120":205,44:2:"|":800:0:0,90279,191ox}2:0,90:" Since the other 2 angleince the other two dogs pulled":"equally hard, the other angles are":"each 30| above the horizontal."mZ}1:162,55:"30":214,55:"30":2:177,56:"|":228,56:"|"nd}6:3:96,50119,50:1:98,31:"30":98,50:"30":2:113,32:"|":113,158,39:"a":234,39:"b":196,55:"c"ElA}1:185,68:"40 N":2lF}0,116:" If we redraw the vectors head to":"tail to show equilibrium, it is":"possible to calculate the magnitude":"of vectors a and b.":800:0:0,90279,191gmP}0,90:" S equilibrium."k<}800:0:0,90279,191:2:0,90:" Vectors in equilibrium give a":"resultant of zero.":1:3:2:140,70260,70200,40140,70:142,70149,74:142,70149,66(l>}197,41197,47:197,41191,38:254,68256,62:254,68246,68:2:,507,54:110,25110,31:110,25103,23:110,75110,69:110,75104,78j(}1:18,34:"40 N":2:31,46:"c":60,34:"P":77,22:"a":77,60:"b"k2}2:0,90:" Since no movement takes place,":"we say that the forces acting on":"point P are in"B":186,111:"C"i|y0,130:" These dogs are pulling on ropes.":"How hard are dogs B and C pulling":"if point P doesn't move?"i|900i} 32i }3:2:0,5060,50110,25:60,50110,75i}1:75,40:"60":2:90,42:"|"Hj}0,507,46:0" It is possible for many forces":"to act on a body and there not":"be movement."h,y1.5:50,92:"}":52,77:"A":74,81:"40 N":2:3:64,96124,96164,76:124,96164,116:123,79:"P":166,72:"{":166,112:"{":141,88:"60|"i6y186,71:,120279,191:3:2:990:gSNS1İ955:">RUN PRACTICE"[g1::3::::3:1igS0S24g0,0:WT$" "S;:W9,WY:1:0,18279,18:0,19279,19:3:2:.5gS1000g1:0,18279,18:0,19279,19:3ggy 31Th"y2:0,30:"3fNI5SSESSFİ950:">RUN INSTRUCTIONS.E"`fNI6SSFİ950:">RUN INSTRUCTIONS.F"nfRR1956wf960fN$"#"(S)N$:N$f0:0,180WX,191:2:0,176:"Please wait...":HI:f0:110,0160,16:3f3:110,0:Sg0:0:S0SNS1ĺ::"There is not an "WT$" "S".":?eS0S24keNI1SSBİ950:">RUN INSTRUCTIONS.A"eNI2SSBSSCİ950:">RUN INSTRUCTIONS.B"eNI3SSCSSDİ950:">RUN INSTRUCTIONS.C"fNI4SSDSSEİ950:">RUN INSTRUCTIONS.DA$d>A$" "į:'dCA$" "İ55000:dEA$""İ57000ydHA$(1)į:D$"#"(S)N$: D$:HI:">RUN TEACHER.MENU"dRA$(2)SS(S0):910d\A$(0)820df:::5:"Which screen? ";WS$:(WS$)S(WS$)dp910d810:SS11eW10:49152)128Ă7c"?":10:I115:(49152)128Ă:755BcA$:Kc800c3:W1W11:WC(228):0:W9,0W920,15:228,WC:W9,0:(W196):2:c 810:WC(228):0:0,180WX,191:c*WW::2:0,176:"Press space bar";:WX,WY::d4:11,0:"?":10:11,0Qb750:A$(8)A$(13)A$" "(A$"0"A$"9")725ybA$(8)į11,0:10:N;:10:710bA$(13)A$" "NN10(A$):9:A$bb750:A$"0"A$"9"740bN(A$):N;:b:10 c"?":10:I120:(N$,2):(N$,1)"0"(N$,1)"9"1702aN$:910Na0:0,150279,191:3:YaF15iaX1,Y1:A$ra.3aX1,Y1:A$a.3::aA:AA64:A1A4700aa10:11,0:"?":10a750:A$"0"A$"9"715bN(A$):N;:9:10/'!` "Instructions.F .`d:(21);`n115,HIG`x$9200`NS34:NI6:SB9:SC16:SD21:SE27:SF31:WW1:WT$"Instruction"`137`">BLOAD^START,A$9200"`$9200`N$`(N$,1)"#"S31:910`N$(N$,2):S(N$)$aN$(             65,25279,153:1:1:3::56950:P10:P202 ߱HDD,1):DD:[ޒ0:177,32264,46:aޱr޲ TRIG TABLEޯ1:1:20,46ޯAA$:2:2:1:޲ TRIG TABLE FROM CALCЄޯ:1:20,46ޯAA$:2:2:1!ޯ:0:165,25279,1DL1DD,1)"."(DN$,DL1DD,1)"1"į265DD9,30M޺(DN$,DL1DD,1):DD:fޒ0:177,32264,46:lޱ}޲ TRIG TABLEޯ1:1:20,46ޯAA$:2:2:1:ƃ޲ TRIG TABLE FROM CALCۃޯ:1:20,46ޯAA$:2:2:1,ޯ:0:11DC055580%ޭ(DN$)DF8DC0ı@ް56990:DN$"0"DN$""`!ޭDC1DN$"":DC0:DF0:NF0y&DN$DN$DA$:56950:Dް56990:DN$"":200,30:"error":uޱvޯ:DN$""56990ӂ}ޭNF1į180,30:"-"1~DL(DN$):DD1DL:263DD9,30:(DN$,56850.ݯ178,95191,105:P1178:P295:56850Wݯ202,95215,105:P1202:P295:56850ݯ226,95239,105:P1226:P295:56850ݯ178,75191,85:P1178:P275:56850Ёݯ202,75215,85:P1202:P275:56850ݯ226,75239,85:P1226:P275:56850 ޭDS56990:56950:|ݰ55400:DN(DA$):DN56740,56750,56760,56770,56780,56790,56800,56810,56820:178,135191,145:P1178:P2135:56850ݯ178,115191,125:P1178:P2115:56850ڀݯ202,115215,125:P1202:P2115:56850ݯ226,115239,125:P1226:P2115:"DC0:NF0:DN$""7ܰ56990:DF1:DN$DN$".":56950:gݰ55400:226,55239,65:P1226:P255:DC1ı~"ݭ(DN$,1)"."DF06ݭ(DN$)2DN$"0":NF0:DF0:56990:56950:;ݭDS1DN$(DN$,(DN$)2)"0"(DN$,(DN$)1,1)" "@DN$(DN$,(DN$)1):HNDD~ܭDR3DNHNDD,~ܭDR4DNHNDDG~NF0:DN0NF1:DNDNx~ܰ55250:DN(DN$):56990:DF0:DN(DN)DF1~HNDN:NF1HNHN~ܰ56950:DR0:~ܰ55400:202,135215,145:P1202:P2135:DF1DC0ı~ܭDC1DN$"":DC0:NF0ܭDN$"0255:DP1:56430:DP0:DS0:DR3:f}۰55400:250,75263,85:P1250:P275:DP1:56430:DP0:DS0:DR4:}Pܰ55400:250,135263,145:P1250:P2135}nDC1:DR0HN(DN$):NF1HNHN:}qܭDR0ı}xDD(DN$):NF1DDDD}ܭDR1DNHNDD~ܭDR2DN2:W|$۰55400:250,115263,125:P1250:P2115:DC1İ56990:NF1:DC0:DN$"0":56950:y|?ۭDN$"0"İ56990:NF1:56950:|AۭDS1(DN$,2)"00"DN$(DN$,(DN$)3)"-00":56990:56950:|BDP1:56430:DP0:DS0:DR1:!}۰55400:250,55263,65:P1250:P6900:E{ٰ56990:DN(DN$):DN(DN):55250:DN(DN$):DN(DN)DF1a{DN$(DN):56950:DC1:{\ڰ55400:202,55215,65:P1202:P255{zڰ56990:HN0:DR0:DS0:NF0:DF0:DN$"0":56950:|ڰ55400:250,95263,105:P1250:P295:DP1:56430:DP0:DS0:DR뷌ᷩz L*#    à ԠԠӠ ĠӠ ӮƠ) Ġ Үՠ Р ˠ Р Ϡ Ϡ Ԡ/Ӯ2 Ӯ 1 Ӯà2 ӮĠ.! ӮŠ&Y285:5000:5500;lX1170:X2195:Y185:Y285:5000:5500elX1275:X2246:Y162:Y262:5000:5550lX1206:X2235:Y145:Y245:5000:5500lX1245:X2275:Y185:Y285:5000:5500lX195:X2120:Y145:Y245:5000:5500 mX155:X255:Y146:Y284:84:5000:56509kLX1195:X2170:Y145:Y245:5000:5550bkVX195:X2120:Y185:Y285:5000:5500k`X125:X25:Y185:Y245:5000:0,515,4512,49kjX1245:X2275:Y145:Y245:5000:5500ktX1235:X2208:Y165:Y265:5000:5550l~X155:X285:Y185:A$" "ī3510.j 0,160:"Press space bar":Aj INTRO INTROTj1:2:0,25j$" ";N$;", this program will":"assist you in understanding":"vectors.":3500j.1:4::5:3j8X155:X285:Y145:Y245:5000:5500kBX1145:X2145:Y146:Y2"Copyright 1987 UAH"6i0,175:"Press space bar"@i3000Fi\i A$:A$" "3010i A$(1)į:HI:">RUN TEACHER.MENU"i 3000i 1i i 2:0,160:"Press space bar"i A$:A$""ĺ">RUN TEACHER.MENU"i A$""ī6000 j 5,20hW"Energy Division"Ch\"Alabama Department of Economic"aha" and Community Affairs"|hf"Montgomery, Alabama"hk0,85hp"Prepared by:"ht5,100hu"Johnson Research Center"hz"University of Alabama in Huntsville"h0,145i!"Science"g$"Energy"+g*"Education"8g/37,120Gg0"Project"Rg1"SEE"kg2170,110:"Vectors"|g42:15,175g5"Press space bar"g>3000gC1gE0,0279,1gG0,80279,81gH0,134279,135gL0,5gM"Distributed by:"hR5,155,165f3+f10,105,1510,18=f10,1815,20Wf15,16910,1675,164rf145,10140,15149,20f15,13145,13f15,16142,16f1f30,30135,32f133,30136,95f30,95135,97f27,3030,97f3f 37,38 g148,20148,170#e147,20147,170Ae18,2118,170:8,198,165He3Xe6,156,165le149,20149,170~e16,2116,170e15,20150,20e15,170150,170:15,169150,169e150,20150,170e15,2015,170e10,9145,9e10,10145,10 fM$"d0,140:"Thank you, "N$"."+dN$Nd2:0,175:"Press space bar"ndA$:A$" "A$(1)1250d0:0,175279,191:3dA$(1)ĺ">RUNTEACHER.MENU"d3600d headerd3d17,2117,170d15,19150,19d7,197,165e)N$""1160.cj(N$)12A$"A"A$"Z"1100DctX((N$)),Y:A$;Wc~N$N$A$:1100kcX((N$)1),80xc(N$,1)cX((N$)1),80c(N$)1N$"":1100cN$(N$,(N$)1):1100d(N$)1M$(N$,1):I2(N$):M$M$(((N$,I))32)::N$rst name and press return.""b14b0,74179,75Ib177,74179,101]b 0,100179,101nb 0,753,101~b2:0,102b"maximum 12 characters"b.7,80b33b8N$""bB49168,0bLA$bVA$(13)N$""1210 c`(A$(8)A$(127)a$0800,2:13,2)a$AE00,3:18,3>a$0000,4:18,4Hab640Yav216,0:1000xa216,0:(222)6ģHI:::a620a1:1a:2a2000a1a0,0279,1a0,40279,41a0,5a"Before we start type"b"your fiV-` "Start '`d(21)/`n::`xX(12)J`">BRUNGAP"^`$9200:$9200w`HI(115)(116)256`6">BLOAD]WAGO,A$800"`@">BLOAD]CHOP,A$A500"`J">BLOAD]BLOCK,A$AE00"`T">BLOAD^START,A$9200"`^768,0`$A500,1:9,1               "Hello 2d43698,190:217,0@n">HIDOS"Ls5:" "XxS24576aS,0w103,1:104,S256">RUN START"U">-START" S24576S,0103,1:104,S256">RUNSTART" VECTORE|LN(((X1X2)2)((Y1Y2)2)):XC(X2X1)LN:YC(Y2Y1)LNQ|X1,Y1^|WW0LN{|X1XCWW,Y1YCWW:WW||| HORZ RIGHT|(X22)X22X2X21|X22,Y2X27,Y24|X22,Y2X27,Y24:| HORZ LEFT }(X22)X255400:.5<{:",-";::55400:P1250:P2115:55400:.5n{ :",=";::55400:P1250:P2135:55400:.5{:" standard":1{ 0,115:"ctrl-k = go to":"calculator":1{*0,145:"ESC = exit calculator":1{43500{4060| DRAW,70:"C = clear all":55400:P1202:P255:55400:2sz0,85:"< = clear last key":55400:P1226:P255:55400:2z0,100:"x";::55400:P1250:P255:55400:.5z:",/";::55400:P1250:P275:55400:.5 {:",+";::55400:P1250:P295:."::"6 + 2 / 4":"will give an":"answer of 2,":"not 6.5.":3500Uy0,0165,191y2:0,10:"Remember these keys:":.5:0,40:"E = exponential":55400:P1178:P255:55400:2y0,55:"R = square root":55400:P1226:P2135:55400:23z0950xNN$:NN$"4"4480Wx55400:P1178:P295:55400:DN$"6.3E-04":56990:56950pxNN$:NN$"="4500x55400:P1250:P2135:55400:DN$"1.89E+24":56990:56950Cy0:0,0165,191:2:0,30:"Operations are":"performed as you":"enter them950wDNN$:NN$"0"4420VwN55400:P1178:P2135:55400:DN$DN$NN$:56990:56950owXNN$:NN$"E"4440wb55400:P1178:P255:55400:DN$DN$NN$"+00":56990:56950wlNN$:NN$"-"4460xv55400:P1250:P2115:55400:DN$"6.3E-00":56990:56.v1:DN$:DN$"x"DN$"X"DN$"*"4372iv55400:P1250:P255:55400:56990:DN$"6.3E+27":56950vDN$:DN$"3"4380v&55400:P1226:P2115:55400:56990:56950v0NN$:NN$"."4400w:55400:P1202:P2135:55400:DN$DN$NN$:56990:565400:DN$"6.3E+02":56990:569509uNN$:NN$"7"4340tu55400:P1178:P275:55400:DN$"6.3E+27":56990:56950u2:0,79:19:"To multiply by":"3.0x10,"u1:48,90:"-4":2:14:0,112:"Type x 3 . 0 E - 4,":"then =.":"Type it now."55400:DN$DN$NN$:56990:569509tNN$:NN$"3"4280st55400:P1226:P2115:55400:DN$DN$NN$:56990:56950tNN$:NN$"E"4300t55400:P1178:P255:55400:DN$DN$NN$"+00":56990:56950tNN$:NN$"2"4320 u55400:P1202:P2115:5r.":3500=sr2:0:0,0165,150:0,30:"To enter 6.3x10,"Ts|1:126,23:"27"s2:14:0,43:"you type 6 . 3 E 2 7":"Type it now.":1sDN$:DN$"6"4240sP1226:P295:55400:56950sNN$:NN$"."4260 t55400:P1202:P2135:een you left"Rr@"to go to the calculator, press":"'ESC'. Now hold the control"rJ"key (ctrl) down and press":"the 'K' key."rTAN$:AN$" "4180r^1:1:2 sh0,30:"This calculator":"has some special":"keys to make your":"work easierogram")qAN$:AN$"1"AN$"2"4110qqAN$"2"į0,150:"One moment please..."::">RUN INSTRUCTIONS.A"yq"1q,0,25:" To make the calculator appear":"on the screen, press 'ctrl-k'." r6"To leave the calculator and":"return to the scr:0,25:" A calculator may be brought":"to the screen by pressing":"ctrl-K. If you need help using":"the calculator, press 1, if not"p"press 2."p22,100:"1. How to use the built-in"p46,115:"calculator"q20,130:"2. Begin the p1:0,25:" ";N$;", as you study this":"lesson on vectors, you may need ":"a table of trig functions. If you":"press ctrl-T a table of the values"oF"you need will appear. Press any":"key to return to the lesson."o3500o INTROp1246:5000:5600:nX1235:X2235:Y145:Y264:5000:5650bn X175:X255:Y165:Y265:5000:5550nX1207:X2207:Y184:Y246:5000:5600nX1169:X2169:Y146:Y284:5000:5650n(X1235:X2220:Y185:Y265:5000:218,73221,67229,69n23500o<5000:56504mX1195:X2195:Y184:Y246:5000:5600\mX195:X295:Y184:Y246:5000:5600mX125:X245:Y185:Y245:5000:49,5245,4537,49mX1275:X2275:Y184:Y263:5000:5600mX1160:X2130:Y145:Y245:5000:5550nX1245:X2245:Y161:Y1DN$"":DC0:DF0:NF0.&DN$DN$DA$:569504CޱAD޲ ERRORgIް56990:DN$"":200,30:"error":muޱzv޲ DISPxޯ{ޭDN$""56990}ޭNF1į180,30:"-"~DL(DN$)njށDD1DLޯ263DD9,30:(DN$,DL1DD,1)"."(DN$,DL1DD,1)2:P295:568507ݯ226,95239,105:P1226:P295:56850_ݯ178,75191,85:P1178:P275:56850ݯ202,75215,85:P1202:P275:56850ݯ226,75239,85:P1226:P275:56850ċޭDS1DC055580܋ޭ(DN$)DF8DC0ıް56990:DN$"0"DN$""!ޭDC6800,56810,56820;ݯ178,135191,145:P1178:P2135:56850fݯ178,115191,125:P1178:P2115:56850ݯ202,115215,125:P1202:P2115:56850ݯ226,115239,125:P1226:P2115:56850ݯ178,95191,105:P1178:P295:56850ݯ202,95215,105:P1205:P1226:P2551ݭDC1ıJ6ݭ(DN$)2DN$"0":NF0:DF0:56990:56950:;ݭDS1DN$(DN$,(DN$)2)"0"(DN$,(DN$)1,1)" "@DN$(DN$,(DN$)1)Jݰ56990:56950{ݱ|ݲ NUMȉݰ55400DN(DA$):DN56740,56750,56760,56770,56780,56790,5HNDN:NF1HNHN'ܰ56950:DR0-ܱ6ܲ .Aܰ55400eܯ202,135215,145:P1202:P2135vܭDF1DC0ıܭDC1DN$"":DC0:NF0ܭDN$"0"DC0:NF0:DN$""҈ܰ56990:DF1:DN$DN$".":56950؈ݱݲ <-"ݰ55400,ݯ226,55239,6263,145:P1250:P2135=nDC1:DR0HN(DN$):NF1HNHN:IqܭDR0ıdxDD(DN$):NF1DDDDwܭDR1DNHNDDܭDR2DNHNDDܭDR3DNHNDDܭDR4DNHNDDˇNF0:DN0NF1:DNDNܰ55250:DN(DN$)ܰ56990:DF0:DN(DN)DF156430:DP0:DS0LDR1۱)۲ X4۰55400Uۯ250,55263,65:P1250:P255oDP1:56430:DP0:DS0xDR3~۱۲ /۰55400ܯ250,75263,85:P1250:P275Ά DP1:56430:DP0:DS0׆DR4݆OܱPܲ =Zܰ55400dܯ250,1350":56950ڱڲ +$ڰ55400Fگ250,95263,105:P1250:P295`DP1:56430:DP0:DS0iDR2o#۱y$۲ -)ۭDC1İ56990:NF1:DC0:DN$"0":56950:Dž+ۭDN$"0"İ56990:NF1:56950:҅.۰554008ۯ250,115263,125:P1250:P2115BDP1:226,135239,145:P1226:P21356DF0:NF1İ56900:eٰ56990:DN(DN$):DN(DN):55250:DN(DN$)y٭DN(DN)DF1DN$(DN):56950DC1Rڱ\ڲ CLEARfڰ55400քpگ202,55215,65:P1202:P255 zڰ56990:HN0:DR0:DS0:NF0:DF0:DN$"N$"0"DS1(DN$)1000ı@DS1:(DN$)DF3DN$(DN$,3DF)f٭(DN$,1)"."DN$(DN$,(DN$)1)DN$DN$"E+00":56990:56950ٱٲ GET E NUMă&DN$(DN$,(DN$)2)(DN$,1)DA$փ0ٰ56990:56950܃ٱٲ SQUARE ROOTٰ55400ٯ22)69(222)133(222)53ij1د::DP1ġ<ذ56900VDR0:NF0:DF0:DN$""agث55050}hز UNINVERSE (VERSE?!?)rدP1,P2P113,P210رز OFFد2:2:1:ز Êٰ55400ٯ178,55191,65:P1178:P255 ٭DC1ı ٭D,(DN$)DU4)ױIDU(DN$)1:DD1(DN$):(DN$,DD,1)"."DUDD1QׂDDDN$(((DN$,3))100)"E+":DU$(DU):DU10DU$"0"DU$DN$DN$DU$:ײ ALREADY EՁ׭(DN$)8DN$(DN$,4)(DN$,4)ہرز ONERR ROUTINE ع216,0:(255100ײ FIX DN $DN$(DN)PDS0:DD1(DN$):(DN$,DD,1)"E"DS1XׂDDh׭DS155280׭DN9999999955270׭(DN$)8DN$(DN$,8):(DN$,1)"."DN$(DN$,7)ׁDD1(DN$):(DN$,DD,1)"."DU(DN$)DDׂDD ׭DU4DN$(DN$İ55550F׭DA$"R"İ55700/P׭DA$"C"İ55900CZ׭DA$"+"İ56000Wd׭DA$"-"İ56100sn׭DA$"X"DA$"*"İ56200x׭DA$"/"İ56300׭DA$"="İ56400׭DA$"."İ56500׭DA$(8)DA$(136)İ56600׭(DA$)0(DA$)48(DA$)176İ56700׫1"~2:0,12:"Press any key"+~A$;~2:2:1E~W3510W~ֲ CALCULATOR~֯:1:1:0:165,25279,153:1:1~DF0:NF0:DC0:DP0~֒3:~P10:P20:DN$"":55930~ ץ55300~<ׯDA$:DA$(27)DA$(155)55500A׭DA$"E"2X2X21"}X22,Y2X27,Y24<}X22,Y2X27,Y24:E} UP_}(X22)X22X2X21u}X2,Y2X25,Y26}X21,Y2X24,Y26:} DOWN}(X22)X22X2X21}&X2,Y2X25,Y26}0X21,Y2X24,Y26:}p TRIG TABLE~z1:900m 2m2:0,30:" When we need to know both":"magnitude and direction as when":"we study forces in physics,":"we represent the forces as"m"vectors. ";:2:800:2:"Vector quantities":"have both magnitude and direction."m 9000,30:" In our everyday lives we refer":"to objects and events as having":"size, or magnitude, such as dollars":"of money or kilometers of distance.":2:800l2:"These magnitudes are scalar,":"meaning that only size is":"measurable.":900mk0:0,120279,191:3:2:990CkSNS1İ955:">RUN PRACTICE"dk1::3::::3:1skS059000k0,0:WT$" "S;:W9,WY:1:0,18279,18:0,19279,19:3:2:.5kS1000k1:0,18279,18:0,19279,19:3kk 1l2:UCTIONS.D"RUN INSTRUCTIONS.E"ijNI6SSFİ950:">RUN INSTRUCTIONS.F"wjRR1956j960jN$"#"(S)N$:N$j0:0,180WX,191:2:0,176:"Please wait...":HI:j0:110,0160,16:3j3:110,0:S!810:SS1HiW10::S0SNS1ĺ::"There is not an "WT$" "S".":tiNI1SSBİ950:">RUN INSTRUCTIONS.A"iNI2SSBSSCİ950:">RUN INSTRUCTIONS.B"iNI3SSCSSDİ950:">RUN INSTRUCTIONS.C" jNI4SSDSSEİ950:">RUN INSTR";:WX,WY::h4A$+h>A$" "į:>hCA$" "İ55000QhEA$""İ57000hHA$(1)į:D$"#"(S)N$: D$:HI:">RUN TEACHER.MENU"hRA$(2)SS(S0):910h\A$(0)820hf:::5:"Which screen? ";WS$:(WS$)S(WS$)hp910 i"?":10:I120:(49152)128ĂNg"?":10:I115:(49152)128Ă:755YgA$:bg800g3:W1W11:WC(228):0:W9,0W920,15:228,WC:W9,0:(W196):2:g 810:WC(228):0:0,180WX,191:h*WW::2:0,176:"Press space bar0fN(A$):N;:9:10:11,0:"?":10:11,0if750:A$(8)A$(13)A$" "(A$"0"A$"9")725fA$(8)į11,0:10:N;:10:710fA$(13)A$" "NN10(A$):9:A$ff750:A$"0"A$"9"740fN(A$):N:f:10#g)"1"):egWLWB:WTWLWLWT9elWX,WY8WXWL3,WY8`eqWX3(WLWT)2,WY8:9:T0ĺTevWX3(WLWB)2,WY6:10:B0ĺBe{WXWL5,WYWS::WS0:eA:AA64:A1A4700ee10:11,0:"?":10e750:A$"0"A$"9"715 WX2(WLWT)2,WY7:9:T0ĺTLdWX2(WLWB)2,WY5:10:B0ĺBkdWXWL3,WYWS::WS0:dX:2:WX,WY:WYWYWSd]WT0:WT$((T)):WI1(WT$):WTWT93((WT$,WI,1)"1"):ebWB0:WB$((B)):WI1(WB$):WBWB93((WB$,WI,1WYWS:305(c:1:WX,WY:WYWYWSzcWT0:WT$((T)):WI1(WT$):WTWT82((WT$,WI,1)"1")((WT$,WI,1)"4"):cWB0:WB$((B)):WI1(WB$):WBWB82((WB$,WI,1)"1")((WB$,WI,1)"4"):cWLWB:WTWLWLWTcWX,WY9WXWL1,WY9$d(WB$):WBWB123((WB$,WI,1)"1"):;b;WLWB:WTWLWLWTkb@WX,WY8WXWL5,WY8:WX,WY9WXWL5,WY9bEWX4(WLWT)2,WY8:9:T0ĺTbJWX4(WLWB)2,WY12:10:B0ĺBbOWXWL8,WYWS::WS0: c:4:WX,WY:WX2((WX2)):WY$,1)"0"(N$,1)"9"170(aN$:910Da0:0,150279,191:3:OaF15_aX1,Y1:A$ha.3xaX1,Y1:A$a.3::a,:3:WX,WY:WYWYWSa1WT0:WT$((T)):WI1(WT$):WTWT123((WT$,WI,1)"1"):$b6WB0:WB$((B)):WI1L0!` "Instructions.A .`d:(21);`n115,HIG`x$9200`NS34:NI1:SB9:SC16:SD21:SE27:SF31:WW1:WT$"Instruction"`">BLOAD^START,A$9200"`$9200`N$`(N$,1)"#"S1:910`N$(N$,2):S(N$)aN$(N$,2):(N                "1"į265DD9,30(޺(DN$,DL1DD,1)0ނDD6ޱOޒ0:177,32264,46:Uޱ0:" If the vector represents force,":"it might show 6 newtons to the":"east."Z}?900b}@ 8}J2:0,30:" Vectors can be added by":"drawing them head to tail and":"measuring the resultant."+~T6:3:X190:X2170:Y1150:Y2150:40100:170,1:40000/|v120,90114,86:120,90114,94:1|0,120:" This vector shows 6 units in":"an easterly direction.":800:0:0,120279,191|0,120:" If the vector represents km,":"it would show 6 km to the east.":800:0,120279,191Q}0,12:"C"{800O{0,145:" Resultant vector C in each":"case is the same."X{W900`{X 7{b2:0,30:" The length of a vector drawn":"to scale represents magnitude,":"with the arrow showing direction."|l2:3:2:X160:X2120:Y190:Y290z5:10,82108,130101,132:108,130105,124:49,108:"C"Fz800z6:152,130250,130244,125:250,130244,135:190,130:"A"z152,82152,129148,123:151,129155,123:162,99:"B"{5:150,82248,128241,130:248,128245,122:206,90136,151:141,157146,151:6%yo900-yp 6yz2:0,30:" The order in which the vectors":"are drawn does not matter.":800y3:6:10,80110,80104,75:110,80104,85:50,63:"A"y112,80112,130108,124:111,130115,124:122,93:"B"=X290:Y1130:Y2110:40000.x^90,11092,116TxhX192:X2192:Y1110:Y2120:40000|xr194,120189,114:194,120189,123x|X1192:X2142:Y1122:Y2157:40000x142,157143,150:142,157150,157y5:X1141:Y1125:X2141:Y2157:40000:141,157Y1147:Y2157:40000w6147,150152,157:145,162152,157:5:X1151:Y1107:X2151:Y2155:40000:151,154145,148:151,154156,148w;800:0:0,100279,191:6w@X1140:X2120:Y1125:Y2130:40000wJ120,130124,124:120,130128,133xTX1118:0:159,151157,144:159,151153,155:61v800Lv0:50,100279,191:6|v150,105110,105116,100:110,105116,110vEE14212210:EE,102EE,108:EEvX1108:X248:Y1105:Y2145:40000v"48,14555,147:48,14548,138w,X149:X2149:vector to the head":"of the last vector."u3:6:60,110160,110154,105:160,110154,115:EE7015010:EE,107EE,113:EEu162,110162,156166,151:161,156157,151uEE1201479:158,EE165,EE:EE(v5:X161:Y1112:X2160:Y2151:4000120:400003tF194,120189,114:194,120189,123ZtPX1192:X2142:Y1122:Y2157:40000tZ142,157143,150:142,157150,157td800:0:0,30279,191:6*un0,30:" The resultant of the vectors is":"a vector drawn from the tail":"of the first :Y1147:Y2157:40000=s 147,150152,157:145,162152,157\s800:0:0,100279,191:6sX1140:X2120:Y1125:Y2130:40000s120,130124,124:120,130128,133s(X1118:X290:Y1130:Y2110:40000s290,11092,116 t<X192:X2192:Y1110:Y2151)rEE1201479:158,EE165,EE:EE2r800Mr0:50,100279,191:6}r150,105110,105116,100:110,105116,110rEE14212210:EE,102EE,108:EErX1108:X248:Y1105:Y2145:40000r48,14555,147:48,14548,138sX149:X2149:" When we add vectors using the":"graphical method, we always put":"the head of one vector to the":"tail of another."q3:6:60,110160,110154,105:160,110154,115:EE7015010:EE,107EE,113:EEr162,110162,156166,151:161,156157,2:"and east, west.":87,67:"W":187,67:"E":800Kp0:0,130279,191p5:0,130:"We show magnitude by equally":"spaced marks on the axes."pEE1091738:EE,72EE,78:EEpEE481029:136,EE144,EE:EEp900p 5{q2:0,30110:100,75180,75vo2:0,130:"We begin by drawing a set of":"perpendicular lines that cross":"to form axes."o800:0:0,130279,191o0,130:"The axes represent the directions":"north, south":24p138,23:"N":138,111:"S":800:n 3n 2:0,30:" When vectors are added, we":"must consider both the magnitude":"and direction of the vectors":"being added. In many cases, it is":"easy to use graphs to solve":"vector problems."n900n 4n3:5o140,40140,226,75239,85:P1226:P275:568506ޭDS1DC055580Nޭ(DN$)DF8DC0ıiް56990:DN$"0"DN$""!ޭDC1DN$"":DC0:DF0:NF0&DN$DN$DA$:56950:ȍDް56990:DN$"":200,30:"error":΍uޱvޯ:DN$""56990}ޭNF1į180,30:"-"Z~850.ݯ226,115239,125:P1226:P2115:56850Wݯ178,95191,105:P1178:P295:56850ݯ202,95215,105:P1202:P295:56850ݯ226,95239,105:P1226:P295:56850ьݯ178,75191,85:P1178:P275:56850ݯ202,75215,85:P1202:P275:56850!ݯ(DN$)1,1)" "7@DN$(DN$,(DN$)1):56990:56950:|ݰ55400:DN(DA$):DN56740,56750,56760,56770,56780,56790,56800,56810,56820:178,135191,145:P1178:P2135:56850؋ݯ178,115191,125:P1178:P2115:56850ݯ202,115215,125:P1202:P2115:56ıܭDC1DN$"":DC0:NF0;ܭDN$"0"DC0:NF0:DN$""`ܰ56990:DF1:DN$DN$".":56950:ݰ55400:226,55239,65:P1226:P255:DC1ı"ݭ(DN$,1)"."DF0׊6ݭ(DN$)2DN$"0":NF0:DF0:56990:56950:;ݭDS1DN$(DN$,(DN$)2)"0"(DN$,1DDDDܭDR1DNHNDD/ܭDR2DNHNDDBܭDR3DNHNDDUܭDR4DNHNDDpNF0:DN0NF1:DNDNܰ55250:DN(DN$):56990:DF0:DN(DN)DF1HNDN:NF1HNHNʉܰ56950:DR0:ܰ55400:202,135215,145:P1202:P2135:DF1DC0R1:J۰55400:250,55263,65:P1250:P255:DP1:56430:DP0:DS0:DR3:۰55400:250,75263,85:P1250:P275:DP1:56430:DP0:DS0:DR4:Pܰ55400:250,135263,145:P1250:P2135nDC1:DR0HN(DN$):NF1HNHN:qܭDR0ı xDD(DN$):NF105:P1250:P295:DP1:56430:DP0:DS0:DR2:$۰55400:250,115263,125:P1250:P2115:DC1İ56990:NF1:DC0:DN$"0":56950:?ۭDN$"0"İ56990:NF1:56950:AۭDS1(DN$,2)"00"DN$(DN$,(DN$)3)"-00":56990:56950:BDP1:56430:DP0:DS0:D6,135239,145:P1226:P2135:DF0:NF1İ56900:nٰ56990:DN(DN$):DN(DN):55250:DN(DN$):DN(DN)DF1DN$(DN):56950:DC1:\ڰ55400:202,55215,65:P1202:P255zڰ56990:HN0:DR0:DS0:NF0:DF0:DN$"0":56950:-ڰ55400:250,95263,55400:178,55191,65:P1178:P255:DC1ıL ٭DN$"0"DS1(DN$)1000ırDS1:(DN$)DF3DN$(DN$,3DF)٭(DN$,1)"."DN$(DN$,(DN$)1)DN$DN$"E+00":56990:56950:DN$(DN$,(DN$)2)(DN$,1)DA$:56990:56950:/ٰ55400:22(DU):DU10DU$"0"DU$)DN$DN$DU$:M׭(DN$)8DN$(DN$,4)(DN$,4)Sرع216,0:(222)69(222)133(222)53ijد::DP1ġذ56900:DR0:NF0:DF0:DN$"":55050߄hحP10įP1,P2P113,P210:P10رد2:2:1::+9999955270A׭(DN$)8DN$(DN$,8):(DN$,1)"."DN$(DN$,7)uDU0:DD1(DN$):(DN$,DD,1)"."DU(DN$)DDׂDD:DU4DN$(DN$,(DN$)DU4)ױփDU(DN$)1:DD1(DN$):(DN$,DD,1)"."DUDD1ׂDD:DN$(((DN$,3))100)"E+":DU$׭DA$"X"DA$"*"İ56200,x׭DA$"/"İ56300@׭DA$"="İ56400T׭DA$"."İ56500t׭DA$(8)DA$(136)İ56600׭(DA$)0(DA$)48(DA$)176İ56700׫55100DN$(DN):DS0:DD1(DN$):(DN$,DD,1)"E"DS1ׂDD:DS155280 ׭DN999:1:0:165,25279,153:1:1:DF0:NF0:DC0:DP0:3::P10:P20:DN$"":55930^ ץ55300<ׯDA$:DA$(27)DA$(155)55500>׭DA$""İ57050A׭DA$"E"İ55550F׭DA$"R"İ55700ԁP׭DA$"C"İ55900Z׭DA$"+"İ56000d׭DA$"-"İ56100n(JC4),Y1REJC(IC3)RE%< MARK DRAWER X2 NX1,Y1X2,Y2LN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNRE19LN1820œX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)꜂RER֯:1The resultant vector C is 5 units":"long and points in northeasterly":"direction."]'#900o@ MARK DRAWEREX1,Y1X2,Y2JLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNTRE8LN810^X1REIC(JC4),Y1REJC(IC3)X1REIC50164,146:170,150164,154:130,155:"A"~^X1172:X2172:Y1150:Y290:40100:171,90167,96:172,90176,96:180,112:"B"~hX190:Y1148:X2168:Y290:5:40100:168,90162,88:168,90166,95:120,95:"C":800~r0:0,25279,80T|0,30:" k0:0,120279,191:3:2:990CkSNS1İ955:">RUN PRACTICE"dk1::3::::3:1skS059000k0,0:WT$" "S;:W9,WY:1:0,18279,18:0,19279,19:3:2:.5kS1000k1:0,18279,18:0,19279,19:3kk(# 9$l2#6:UCTIONS.D"RUN INSTRUCTIONS.E"ijNI6SSFİ950:">RUN INSTRUCTIONS.F"wjRR1956j960jN$"#"(S)N$:N$j0:0,180WX,191:2:0,176:"Please wait...":HI:j0:110,0160,16:3j3:110,0:S!810:SS1HiW10::S0SNS1ĺ::"There is not an "WT$" "S".":tiNI1SSBİ950:">RUN INSTRUCTIONS.A"iNI2SSBSSCİ950:">RUN INSTRUCTIONS.B"iNI3SSCSSDİ950:">RUN INSTRUCTIONS.C" jNI4SSDSSEİ950:">RUN INSTR";:WX,WY::h4A$+h>A$" "į:>hCA$" "İ55000QhEA$""İ57000hHA$(1)į:D$"#"(S)N$: D$:HI:">RUN TEACHER.MENU"hRA$(2)SS(S0):910h\A$(0)820hf:::5:"Which screen? ";WS$:(WS$)S(WS$)hp910 i"?":10:I120:(49152)128ĂNg"?":10:I115:(49152)128Ă:755YgA$:bg800g3:W1W11:WC(228):0:W9,0W920,15:228,WC:W9,0:(W196):2:g 810:WC(228):0:0,180WX,191:h*WW::2:0,176:"Press space bar0fN(A$):N;:9:10:11,0:"?":10:11,0if750:A$(8)A$(13)A$" "(A$"0"A$"9")725fA$(8)į11,0:10:N;:10:710fA$(13)A$" "NN10(A$):9:A$ff750:A$"0"A$"9"740fN(A$):N:f:10#g)"1"):egWLWB:WTWLWLWT9elWX,WY8WXWL3,WY8`eqWX3(WLWT)2,WY8:9:T0ĺTevWX3(WLWB)2,WY6:10:B0ĺBe{WXWL5,WYWS::WS0:eA:AA64:A1A4700ee10:11,0:"?":10e750:A$"0"A$"9"715 WX2(WLWT)2,WY7:9:T0ĺTLdWX2(WLWB)2,WY5:10:B0ĺBkdWXWL3,WYWS::WS0:dX:2:WX,WY:WYWYWSd]WT0:WT$((T)):WI1(WT$):WTWT93((WT$,WI,1)"1"):ebWB0:WB$((B)):WI1(WB$):WBWB93((WB$,WI,1WYWS:305(c:1:WX,WY:WYWYWSzcWT0:WT$((T)):WI1(WT$):WTWT82((WT$,WI,1)"1")((WT$,WI,1)"4"):cWB0:WB$((B)):WI1(WB$):WBWB82((WB$,WI,1)"1")((WB$,WI,1)"4"):cWLWB:WTWLWLWTcWX,WY9WXWL1,WY9$d(WB$):WBWB123((WB$,WI,1)"1"):;b;WLWB:WTWLWLWTkb@WX,WY8WXWL5,WY8:WX,WY9WXWL5,WY9bEWX4(WLWT)2,WY8:9:T0ĺTbJWX4(WLWB)2,WY12:10:B0ĺBbOWXWL8,WYWS::WS0: c:4:WX,WY:WX2((WX2)):WY$,1)"0"(N$,1)"9"170(aN$:910Da0:0,150279,191:3:OaF15_aX1,Y1:A$ha.3xaX1,Y1:A$a.3::a,:3:WX,WY:WYWYWSa1WT0:WT$((T)):WI1(WT$):WTWT123((WT$,WI,1)"1"):$b6WB0:WB$((B)):WI1/!` "Instructions.B .`d:(21);`n115,HIG`x$9200`NS34:NI2:SB9:SC16:SD21:SE27:SF31:WW1:WT$"Instruction"`">BLOAD^START,A$9200"`$9200`N$`(N$,1)"#"S9:910`N$(N$,2):S(N$)aN$(N$,2):(N               s program"2"will assist you in understanding"B"vectors."K900H0,46ޯAA$:2:2:1Uޯ:0:165,25279,153:1:1:3::56950:P10:P20[ ߱xNI1S0SNB(NI2)NC(NI3)ND(NI4)NE(NI5):9101:0,50279,50:0,51279,51̏0,115279,115ߏ0,116279,116珎毾20,60 N$", thiDL(DN$):DD1DL:263DD9,30:(DN$,DL1DD,1)"."(DN$,DL1DD,1)"1"į265DD9,30v޺(DN$,DL1DD,1):DD:ޒ0:177,32264,46:ޱ޲ TRIG TABLEޯ1:1:20,46ӎޯAA$:2:2:1:޲ TRIG TABLE FROM CALCޯ:1:2100P{:0,30:" For every 9 km the plane moved":"east, it moved 4 km south."k{:800:4:0,30279,100{:0,30:" The path of the plane can be":"shown by a vector."{:X182:X2171:Y1112:Y2161:7:3:40300:171,160164,163:171,160168,1541,110165,114Rz:X180:X280:Y1110:Y2160:40300:80,16076,154:79,16083,154sz:177,101:"E":77,162:"S"z:3:QQ2901:4:QQ80,(QQ59)111QQ80,(QQ59)111:7:QQ81,((QQ1)59)111QQ81,((QQ1)59)111:QQ{:800:4:0,30279, look at an example."y:900'y: 15y:2:0,30:" If a plane flies east 90 km":"and is blown 50 km south by a":"strong north wind while doing":"so, where will its position be?" z:X181:X2171:Y1110:Y2110:6:3:40300:171,110165,106:17135:" At the end of your walk you":"are 2.8 km northwest of":"your starting point."`x6900ix6 14y62:0,30:" Although it is possible to":"find a resultant using a":"graphical solution, we usually":"use a mathematical solution.":" Let's:1)w398,7098,35:106,44:"4":8009w32:2:1iwX45:X1180:X2102:Y1108:Y230:40000:40200wb4102,30100,37102,34:102,32109,32wl40,135:2:" The resultant is 2.8 km long and":"points morthwest.":800:0:0,135279,191Wxv40,106Dv2X198:X298:Y1110:Y230:40200:97,30101,36:98,3094,36Lv21v20,135:" You have walked a total of":"4 km in all."v37:144,110181,110:1:158,92:"1":1v3104,110138,110:120,92:"2":1w398,11098,73:106,82:"3"00:0:0,30279,191u.0,30:" You walk 2 km due west, then":"turn north and walk another 2 km.":"Where are you with respect to":"your starting point."u2900u2 13v26:X1180:X2100:Y1110:Y2110:3:40200:100,110106,114:100,110106,| is close to 0.8,":"so the angle ] is about 36|."Ot+800:0:0,120279,191t+0,120:" The resultant is 5 units long":"and points 36| north of east."t.900t. 12t.2:0,30:" Let's work a problem using":"a graphical solution."u.841,143]s+155,135:"=":173,127:"4":173,143:"5":170,143183,143:197,135:"= 0.8"s+2:0,160:"Press ctrl-T and see what angle":"has a cosine of 0.8"s+AS$:AS$""11170s+57000:0:0,120279,1913t+0,120:" The cosine of 36ctors A and C meet is angle ],":"then"9ra+103,83:"]"Srf+60,155:"cosine] ="rp+151,148:"length A":151,164:"length C":1:3:146,164216,164rz+800:0:0,120279,191s+40,135:"cosine] =":131,127:"A":131,143:"C":1:127,143198:Y240:40100Aq>+159,40159,44:159,40152,38:110,51:"C"qH+0,120:" To find the exact direction in":"which vector C points, we must use":"trigometric functions."qR+800:0:0,120279,191'r\+0,120:" If we assume the point where":"ve 35 or 36 degrees."p*900%p* 11Rp+6:3:X180:X2160:Y1100:Y2100:40100p +160,100154,96:160,100154,104:2:117,105:"A"p+X1162:X2162:Y1100:Y240:40100p +162,40158,45:161,40165,45p*+172,61:"B"q4+5:X179:X2158:Y1YCR(G)!o'120XC,103YC:G4o'158,9082,90xo'1:156,66:"30":144,55:"45":112,44:"90":163,80:"15"o'118,41118,46:158,60162,56:167,70172,67o'174,84180,82p'2:0,120:" This protractor shows the angle":"to be about202,40198,45:201,40205,453nL'119,98198,40WnV'199,40199,44:199,40192,38{n`'R60:PI4(1):7:3:180,102nj'G.07PI.09:XCR(G):YCR(G)nt'120XC,103YC:Gn~'60,102180,102n'R40:158,90 o'G.37PI.3.07:XCR(G):52,38:110,51:"C"%ms#103,83:"]"mx#0,130:" To find the directions in":"which vector C points, measure":"angle ] with a protractor."m'900m' 10m'6:3:120,100200,100m$'200,100194,96:200,100194,104m.'202,100202,40n8'3:X180:X2160:Y1100:Y2100:40100^l<#160,100154,96:160,100154,104:2:117,105:"A"lF#X1162:X2162:Y1100:Y240:40100lP#162,40158,45:161,40165,45lZ#172,61:"B"ld#5:X179:X2158:Y198:Y240:40100mn#159,40159,44:159,4010,56800,56810,56820:178,135191,145:P1178:P2135:56850eݯ178,115191,125:P1178:P2115:56850ݯ202,115215,125:P1202:P2115:56850ݯ226,115239,125:P1226:P2115:56850ݯ178,95191,105:P1178:P295:56850 ݯ202,95215,105:P12025239,65:P1226:P255:DC1ı4"ݭ(DN$,1)"."DF0d6ݭ(DN$)2DN$"0":NF0:DF0:56990:56950:;ݭDS1DN$(DN$,(DN$)2)"0"(DN$,(DN$)1,1)" "Ċ@DN$(DN$,(DN$)1):56990:56950::|ݰ55400:DN(DA$):DN56740,56750,56760,56770,56780,5679ܰ55250:DN(DN$):56990:DF0:DN(DN)DF1EHNDN:NF1HNHNWܰ56950:DR0:ܰ55400:202,135215,145:P1202:P2135:DF1DC0ıܭDC1DN$"":DC0:NF0ȉܭDN$"0"DC0:NF0:DN$""ܰ56990:DF1:DN$DN$".":56950:ݰ55400:226,5DP1:56430:DP0:DS0:DR4:GPܰ55400:250,135263,145:P1250:P2135onDC1:DR0HN(DN$):NF1HNHN:{qܭDR0ıxDD(DN$):NF1DDDDܭDR1DNHNDDܭDR2DNHNDDψܭDR3DNHNDD∠ܭDR4DNHNDDNF0:DN0NF1:DNDN."0":56950:/?ۭDN$"0"İ56990:NF1:56950:qAۭDS1(DN$,2)"00"DN$(DN$,(DN$)3)"-00":56990:56950:BDP1:56430:DP0:DS0:DR1:ׇ۰55400:250,55263,65:P1250:P255:DP1:56430:DP0:DS0:DR3:۰55400:250,75263,85:P1250:P275:DN$(DN):56950:DC1:?\ڰ55400:202,55215,65:P1202:P255tzڰ56990:HN0:DR0:DS0:NF0:DF0:DN$"0":56950:ڰ55400:250,95263,105:P1250:P295:DP1:56430:DP0:DS0:DR2: $۰55400:250,115263,125:P1250:P2115:DC1İ56990:NF1:DC0:DN$%٭(DN$,1)"."DN$(DN$,(DN$)1)HDN$DN$"E+00":56990:56950:}DN$(DN$,(DN$)2)(DN$,1)DA$:56990:56950:ٰ55400:226,135239,145:P1226:P2135:DF0:NF1İ56900:ٰ56990:DN(DN$):DN(DN):55250:DN(DN$):DN(DN)DF1133(222)53ij!د::DP1ġIذ56900:DR0:NF0:DF0:DN$"":55050lhحP10įP1,P2P113,P210:P10rرد2:2:1::ذ55400:178,55191,65:P1178:P255:DC1ıل ٭DN$"0"DS1(DN$)1000ıDS1:(DN$)DF3DN$(DN$,3DF)DD'ׂDD:DU4DN$(DN$,(DN$)DU4)-ױcDU(DN$)1:DD1(DN$):(DN$,DD,1)"."DUDD1ׂDD:DN$(((DN$,3))100)"E+":DU$(DU):DU10DU$"0"DU$DN$DN$DU$:ڃ׭(DN$)8DN$(DN$,4)(DN$,4)رع216,0:(222)69(222)0,׭(DA$)0(DA$)48(DA$)176İ567007׫55100mDN$(DN):DS0:DD1(DN$):(DN$,DD,1)"E"DS1ׂDD:DS155280׭DN9999999955270΂׭(DN$)8DN$(DN$,8):(DN$,1)"."DN$(DN$,7)DU0:DD1(DN$):(DN$,DD,1)"."DU(DN$)DA$(155)55500%>׭DA$""İ570509A׭DA$"E"İ55550MF׭DA$"R"İ55700aP׭DA$"C"İ55900uZ׭DA$"+"İ56000d׭DA$"-"İ56100n׭DA$"X"DA$"*"İ56200x׭DA$"/"İ56300́׭DA$"="İ56400၌׭DA$"."İ56500׭DA$(8)DA$(136)İ5660IC(X2X1)LN:JC(Y2Y1)LN-RE9LN710sX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3){REƝ߀֯:1:1:0:165,25279,153:1:1:DF0:NF0:DC0:DP0:3::P10:P20:DN$"":55930 ץ55300<ׯDA$:DA$(27) X1,Y1X2,Y2PLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNdRE39LN1040&X1REIC(JC7),Y1REJC(IC6)X1REIC(JC7),Y1REJC(IC6)NREbl MARK DRAWERqX1,Y1X2,Y2vLN(((X1X2)2)((Y1Y2)2)):JC(IC3)~RE~/~ MARK DRAWER X2 A~X1,Y1X2,Y2~LN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LN~RE20LN1820~œX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)~꜂RE~ MARK DRAWER X4 nt.":"The displacement of the plane is":"shown by the center vector."P}>900b}@ MARK DRAWERt}EX1,Y1X2,Y2}JLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LN}TRE8LN810 ~^X1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1RE|;800:4:0,30279,100|;0,30:" Notice the lines all have arrows":"on the ends. Vectors always have":"arrows on the end to show":"direction."|;800:4:0,30279,100G}$;0,30:" The length and direction of a":"vector indicate displaceme08103,108:43,12637,112Cj>1:57,105:"2":94,105:"2":.5j>2:0,136:"c = 90 + 50":3:2:43,15143,133123,133:43,15137,137:1:69,130:"2":117,130:"2":.5k?2:140,136:"= 8100 + 2500":160,152160,134270,134:160 plane":"traveled, we can use the":"Pythagorean Theorem,"i>56,149:"c = a + b":3:2:99,16699,148159,148:99,16693,152i>1:113,145:"2":150,145:"2"i>800:0:0,100279,191j>2:0,109:"c = a + b":3:2:43,12643,13:40300:171,30165,26:171,30165,34hh>X180:X280:Y130:Y280:40300:80,8076,74:79,8083,74h>177,21:"90 E":70,82:"50 S"h>X182:X2171:Y132:Y281:7:3:40300:171,80164,83:171,80168,74;i>0,100:" To find out how far the2:990)gSNS1İ955:">RUN PRACTICE"Jg1::3::::3:1YgS059000g0,0:WT$" "S;:W9,WY:1:0,18279,18:0,19279,19:3:2:.5gS1000g1:0,18279,18:0,19279,19:3gg> 16)h>X181:X2171:Y130:Y230:6:ESSFİ950:">RUN INSTRUCTIONS.E"OfNI6SSFİ950:">RUN INSTRUCTIONS.F"]fRR1956ff960~fN$"#"(S)N$:N$f0:0,180WX,191:2:0,176:"Please wait...":HI:f0:110,0160,16:3f3:110,0:Sg0:0,120279,191:3:S0SNS1ĺ::"There is not an "WT$" "S".":ZeNI1SSBİ950:">RUN INSTRUCTIONS.A"eNI2SSBSSCİ950:">RUN INSTRUCTIONS.B"eNI3SSCSSDİ950:">RUN INSTRUCTIONS.C"eNI4SSDSSEİ950:">RUN INSTRUCTIONS.D""fNI5SSd>A$" "į:$dCA$" "İ550007dEA$""İ57000vdHA$(1)į:D$"#"(S)N$: D$:HI:">RUN TEACHER.MENU"dRA$(2)SS(S0):910d\A$(0)820df:::5:"Which screen? ";WS$:(WS$)S(WS$)dp910d810:SS1.eW10::52)128Ă4c"?":10:I115:(49152)128Ă:755?cA$:Hc800c3:W1W11:WC(228):0:W9,0W920,15:228,WC:W9,0:(W196):2:c 810:WC(228):0:0,180WX,191:c*WW::2:0,176:"Press space bar";:WX,WY::c4A$11,0:"?":10:11,0Nb750:A$(8)A$(13)A$" "(A$"0"A$"9")725vbA$(8)į11,0:10:N;:10:710bA$(13)A$" "NN10(A$):9:A$bb750:A$"0"A$"9"740bN(A$):N;:b:10 c"?":10:I120:(4912):(N$,1)"0"(N$,1)"9"170/aN$:910Ka0:0,150279,191:3:VaF15faX1,Y1:A$oa.3aX1,Y1:A$a.3::aA:AA64:A1A4700aa10:11,0:"?":10a750:A$"0"A$"9"715bN(A$):N;:9:10:0`'` "Instructions.C 4`d:(21)A`n115,HIM`x$9200`NS34:NI3:SB9:SC16:SD21:SE27:SF31:WW1:WT$"Instruction"`">BLOAD^START,A$9200"`$9200`N$`(N$,1)"#"S16:910`N$(N$,2):S(N$)!aN$(N$,                2)NC(NI3)ND(NI4)NE(NI5):910F1:0,50279,50:0,51279,51Y0,115279,115l0,116279,116t毾20,60N$", this program""will assist you in understanding"Ϗ"vectors."؏900HD:ޒ0:177,32264,46:"ޱ3޲ TRIG TABLEHޯ1:1:20,46`ޯAA$:2:2:1:|޲ TRIG TABLE FROM CALCޯ:1:20,46ޯAA$:2:2:1ޯ:0:165,25279,153:1:1:3::56950:P10:P20 ߱%xNI1S0SNB(NIDN$"":DC0:DF0:NF0/&DN$DN$DA$:56950:UDް56990:DN$"":200,30:"error":[uޱqvޯ:DN$""56990}ޭNF1į180,30:"-"~DL(DN$):DD1DL:263DD9,30:(DN$,DL1DD,1)"."(DN$,DL1DD,1)"1"į265DD9,30޺(DN$,DL1DD,1):D:P295:568506ݯ226,95239,105:P1226:P295:56850^ݯ178,75191,85:P1178:P275:56850ݯ202,75215,85:P1202:P275:56850ݯ226,75239,85:P1226:P275:56850ÌޭDS1DC055580یޭ(DN$)DF8DC0ıް56990:DN$"0"DN$""!ޭDC126,138 zFK16,157:"= 7.6 km":CzPK800:2:73,29:"7.6 km":2zZK110,85:"cosine ] =":200,78:"7.0 km":200,92:"7.6 km":1:3:198,93247,93zdK180,115:"= .921":141,135:".921 \ cos 23|"={nK800:0:0,82279,191:0,90:" You would 5:"7.0 km"8yK5:87,58156,30154,36:156,30149,28ty(K2:0,86:"C = A + B":1:47,80:"2":85,80:"2"y2K3:2:94,8432,8433,10024,88zs,G0,110:"C = A + B"s6G3:2:93,10931,10931,12427,111:1:47,104:"2":85,104:"2"s@G2:16,130:"= 121 + 30.25":130,13131,13131,14427,133:16,149:"= 151.25"tJG87,15031,15031,16227,15,18WrF2:110,20:"11.0 meters":3:6:95,38205,38:96,38102,32:96,38101,43}rG93,3893,9398,88:94,9389,88rG0,55:"5.5 meters":78,29:"W":78,83:"S"rG3:5:206,4097,9199,84:97,91103,94:129,56:2:"C":172,38:"]"$)/qFCO0:DD12DD12.5PH26PH28CO1vqFCO1į0,150:"Your answer is correct.":"Let's do another.":900qF0,150:"Our answers aren't the same.":"Watch me work the problem."qF800:1:3:0,0:"Instruction 18a"rF3:1:0,18279and ctrl-T."(pF800:0:0,100279,191LpF0,100:"Enter distance: ";:ipF1:3:125,117195,117pF:N7:AA0:A11:AA$".":58000pFDD(A$)pF0,130:"Enter";::50,147100,147:110,130:"degrees S of W."qF:" ";:N5:58000:PH(AdF93,3893,9398,88:94,9389,88WonF0,55:"5.5 meters":78,29:"W":105,83:"S" pxF0,100:" Find the displacement of a ball":"that rolled 11.0 meters west across":"the side of a hill, and 5.5 meters":"south down the hill. Remember":"ctrl-K "be sure you can add vectors.":"Remember that you can get a":"calculator by pressing ctrl-K":"and a table of trig functions":"by pressing ctrl-T."nOF900nPF 18nZF2:110,20:"11.0 meters":3:6:95,38205,38:96,38102,32:96,38101,43#o0,120:" The angle having a cosine":"of .8738 is about 29|."Tm?133,32:"= 29|"pm?800:0:0,100279,191m?0,120:" The plane flew 103 km in a":"direction 29| south of east."mgB900mhB 17nrB2:0,30:" Let's try a few problems to":5:"side adjacent to angle"7l\?1:3:98,162272,162Xlf?140,162:"hypotenuse":800olp?0:0,145279,191lz?10,151:"cosine] =":106,144:"90":100,158:"103":1:3:98,159130,159l?148,151:"= .8738"l?800:0:0,100279,191>m?,152154,138:.51k ?2:0,159:"c = 103 km"Mk*?800:0:0,100279,191sk4?2:175,80:"103":116,32:"]"k>?2:0,100:" To find the direction the plane":"flew, we can use the cosine":"function where"kH?10,151:"cosine ="lR?100,148:P2115:56850:ݯ202,115215,125:P1202:P2115:56850eݯ226,115239,125:P1226:P2115:56850ݯ178,95191,105:P1178:P295:56850ݯ202,95215,105:P1202:P295:56850ݯ226,95239,105:P1226:P295:56850ݯ178,75191,85:P1178:P2756990:56950:F;ݭDS1DN$(DN$,(DN$)2)"0"(DN$,(DN$)1,1)" "n@DN$(DN$,(DN$)1):56990:56950:|ݰ55400:DN(DA$):DN56740,56750,56760,56770,56780,56790,56800,56810,56820:178,135191,145:P1178:P2135:56850ݯ178,115191,125:P1179ܰ55400:202,135215,145:P1202:P2135:DF1DC0ıTܭDC1DN$"":DC0:NF0rܭDN$"0"DC0:NF0:DN$""ܰ56990:DF1:DN$DN$".":56950:Ljݰ55400:226,55239,65:P1226:P255:DC1ıވ"ݭ(DN$,1)"."DF06ݭ(DN$)2DN$"0":NF0:DF0:HN(DN$):NF1HNHN:%qܭDR0ı@xDD(DN$):NF1DDDDSܭDR1DNHNDDfܭDR2DNHNDDyܭDR3DNHNDDܭDR4DNHNDDNF0:DN0NF1:DNDN؇ܰ55250:DN(DN$):56990:DF0:DN(DN)DF1HNDN:NF1HNHNܰ56950:DR0:$)3)"-00":56990:56950:׭DA$""İ57050A׭DA$"E"İ55550F׭DA$"R"İ55700 P׭DA$RE39LN1040T~&X1REIC(JC7),Y1REJC(IC6)X1REIC(JC7),Y1REJC(IC6)\~NREb~bu~l MARK DRAWER~qX1,Y1X2,Y2~vLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LN~RE9LN710X1REIC(JC4),Y1REJC(IC3)X1((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LN=}RE20LN1820}œX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)}꜂RE}} MARK DRAWER X4 } X1,Y1X2,Y2}LN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LN~ MARK DRAWER|EX1,Y1X2,Y2\|JLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNn|TRE8LN810|^X1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)|RE|| MARK DRAWER X2 |X1,Y1X2,Y2)}LN(((X1X2)2)travel 7.6 km in":"a direction 23 degrees north":"of east."F{N900P{ N 20{*N2:0,30:" One use of vector addition in":"physics is finding the resultant of":"several forces acting on a body."{R900{R 21{U900{U 22{Y900 |@,65151,60:156,65151,70hR86,64110,29103,31:110,29112,34:1:42,31:"a = 40 N":91,62:"b = 60 N":165,54:"east":2:99,49:"60|"hlR2:0,90:" If two forces act on a block":"as shown, what is the resultant":"force?":800:0HivR0#gSNS1İ955:">RUN PRACTICE"Dg1::3::::3:1SgS059000g0,0:WT$" "S;:W9,WY:1:0,18279,18:0,19279,19:3:2:.5gS1000g1:0,18279,18:0,19279,19:3ggR 21hR2:60,5585,75:3:3:86,65156İ950:">RUN INSTRUCTIONS.E"IfNI6SSFİ950:">RUN INSTRUCTIONS.F"WfRR1956`f960xfN$"#"(S)N$:N$f0:0,180WX,191:2:0,176:"Please wait...":HI:f0:110,0160,16:3f3:110,0:Sg0:0,120279,191:3:2:99NS1ĺ::"There is not an "WT$" "S".":TeNI1SSBİ950:">RUN INSTRUCTIONS.A"eNI2SSBSSCİ950:">RUN INSTRUCTIONS.B"eNI3SSCSSDİ950:">RUN INSTRUCTIONS.C"eNI4SSDSSEİ950:">RUN INSTRUCTIONS.D"fNI5SSESSF$" "į:dCA$" "İ550001dEA$""İ57000pdHA$(1)į:D$"#"(S)N$: D$:HI:">RUN TEACHER.MENU"dRA$(2)SS(S0):910d\A$(0)820df:::5:"Which screen? ";WS$:(WS$)S(WS$)dp910d810:SS1(eW10::S0S8Ă.c"?":10:I115:(49152)128Ă:7559cA$:Bc800c3:W1W11:WC(228):0:W9,0W920,15:228,WC:W9,0:(W196):2:c 810:WC(228):0:0,180WX,191:c*WW::2:0,176:"Press space bar";:WX,WY::c4A$ d>A"?":10:11,0Hb750:A$(8)A$(13)A$" "(A$"0"A$"9")725pbA$(8)į11,0:10:N;:10:710bA$(13)A$" "NN10(A$):9:A$bb750:A$"0"A$"9"740bN(A$):N;:b:10c"?":10:I120:(49152)12N$,1)"0"(N$,1)"9"170)aN$:910Ea0:0,150279,191:3:PaF15`aX1,Y1:A$ia.3yaX1,Y1:A$a.3::aA:AA64:A1A4700aa10:11,0:"?":10a750:A$"0"A$"9"715bN(A$):N;:9:10:11,0:,!` "Instructions.D .`d:(21);`n115,HIG`x$9200`NS34:NI4:SB9:SC16:SD21:SE27:SF31:WW1:WT$"Instruction"`">BLOAD^START,A$9200"`$9200`N$`(N$,1)"#"S21:910`N$(N$,2):S(N$)aN$(N$,2):(                !!! ! ""vectors."900HX((A$)),Y:A1$;*&A$A$A1$:58020gxNI1S0SNB(NI2)NC(NI3)ND(NI4)NE(NI5):9101:0,50279,50:0,51279,510,115279,1150,116279,116毾20,60ُN$", this program""will assist you in understandingY(A$,1)!X((A$)1),YH⯭(A$)1A$"":A$(A$,(A$)1)S58020f(A$)N58020AAA1$"A"A1$"Z"A1$((A1$)32(AA1)):58140A1A1$"0"A1$"9"58140Ҏ AA$""58020I11(AA$):A1$(AA$,I1,1)Ă:58020:2:1:&޲ TRIG TABLE FROM CALC;ޯ:1:20,46QޯAA$:2:2:1ޯ:0:165,25279,153:1:1:3::56950:P10:P20 ߱A$"":49168,0A1$ǍA1$(13)A$""ıA1$(8)A1$(127)A$""58100X((A$)1),uޱvޯ:DN$""569903}ޭNF1į180,30:"-"~DL(DN$):DD1DL:263DD9,30:(DN$,DL1DD,1)"."(DN$,DL1DD,1)"1"į265DD9,30޺(DN$,DL1DD,1):DD:ƌޒ0:177,32264,46:̌ޱ݌޲ TRIG TABLEޯ1:1:20,46 ޯAA$:25:568500ݯ202,75215,85:P1202:P275:56850Xݯ226,75239,85:P1226:P275:56850mޭDS1DC055580ޭ(DN$)DF8DC0ıް56990:DN$"0"DN$""!ޭDC1DN$"":DC0:DF0:NF0ً&DN$DN$DA$:56950:Dް56990:DN$"":200,30:"error":Qxb133,120:"cos ] =":205,114:"x":205,125:"c":6:3:201,129213,129xb205,138:"80":205,152:"87":201,153223,153:187,144:"=":187,167:"= .9195":800:0:0,100279,191y8c0,100:" Press ctrl-T to see what":"angle has a cosi2:99,71:"]"wpb2:0,100:" Now let's find the angle, ], that":"vector C makes with vector x.":800:0:0,100279,191xb2:0,100:" Angle ] can be found from the":0,120:"cosine of :":3:6:78,12992,129:82,114:"x":82,125:"c",10197,10197,11791,103:122,97:1:"2":193,97:"2":2{vb82,123:"= 6400 + 1200":205,12397,12397,13693,126v b82,142:"= 7600":143,14298,14298,15593,145:82,160:"= 87 N":1:1:81,40:"c = 87 N":800:0:0,100279,191w>b"y = 34.64 N"ua2:0,100:" Since we now have a right":"triangle, we can use the":"Pythagorean theorum to find":"the resultant C.":2:5:69,84187,35180,32:187,35ua800:0:0,100279,191=v b2:60,104:"C = 80 + 34.64":6:3:200components together:"ltt^0,142:"V = 34.64 N + 0.0 N = 34.64 N":0,157:"H = 20 N + 60 N = 80 N"uta900ta 25ta2:3:70,86190,86183,82:190,86183,90:192,86192,34196,39:191,34187,39 ua1:90,82:"x = 80.0 N":198,50:"x = 20 N":800s`^0:0,100279,191:2:0,100:" Since vector b is pointing east,":"it is horizontal and has no vertical":"component.":800:0:0,100279,191tj^2:0,100:" We now add the vertical":"components together and the":"horizontal N x .866":61,162:"= 34.64 N":1:109,45:"y = 34.64 N":800rL^0:0,100279,191:2:0,100:" The horizontal component, x,":"of vector a is:":40,126:"x = 40 N x cos 60|"sV^61,144:"= 40 N x 0.5":61,162:"= 20 N":1:89,80:rop a vertical line from the":"head of vector a to vector b.":1.5:2:104,64:"|":2:104,37104,80q.^800:0:0,100279,191:2:0,100:" The vertical component, y, of":"vector a is:"q8^40,126:"y = 40 N x sin 60|"CrB^61,144:"= 40 p] 245p]3:3:X180:X2152:Y180:Y280:40100kp]152,80146,75:152,80146,85:1:120,63:"b"p^3:3:X180:X2104:Y178:Y234:40100p^104,3496,36:104,34106,40:1:89,63:"60":94,53:"a":2:104,64:"|"hq$^2:0,100:" Decond way to find the":"resultant vector is mathematical."oZ2:2:0,110:" Since we know that force a":"is 40 N and makes an angle of 60|":"with force b, we can resolve force"o Z"a into horizontal and vertical":"component vectors."o]900Y(768)1Ĺ768,0:S29 nY900)nY 23mnY2:60,8585,105:3:3:86,95156,95151,90:156,95151,100nY86,94110,59103,61:110,59112,64:1:42,61:"a = 40 N":91,92:"b = 60 N":165,84:"east":2:99,79:"60|";oY2:0,25:" The s123,79:"c":2m|V0,133:" The resultant vector, c, is 87":"units long and makes an angle of":"24 degrees with vector b.":800:0:0,135279,191mV2:0,133:" The resultant force is 87":"newtons at an angle 24 degrees":"north of east."n0,133:" The tail of vector a is drawn":"from the head of vector b at an":"angle of 60 degrees N of E.":800:4:0,135279,191l^V1:X180:X2177:Y1118:Y274:40100lhV177,75169,71:177,75176,80mrV1:108,103:"24":2:123,104:"|":1:":"represents 60 N acting in an":"easterly direction.":800:0:0,135279,191k6V3:6:160,120180,120:190,120210,120k@V3:3:X1152:X2179:Y1118:Y274:40100kJV180,74172,76:180,74182,80:2:167,103:"60|":1:175,85:"a"lTV2:3,31:110,29112,34:1:42,31:"a = 40 N":91,62:"b = 60 N":165,54:"east":2:99,49:"60|"jV3:3:X180:X2152:Y1120:Y2120:40100jV152,120146,115:152,120146,125:1:113,120:"b"Pk,V2:0,133:" Let 1 cm = 10 newtons. Vector b0,80279,191:0,90:" There are three ways to find":"the resultant."iR800:0,80279,191:0,90:" The first way is a graphical":"solution."iU900iU 22iU2:60,5585,75:3:3:86,65156,65151,60:156,65151,70djV86,64110,2910ݯ226,75239,85:P1226:P275:568509ޭDS1DC055580Qޭ(DN$)DF8DC0ılް56990:DN$"0"DN$""!ޭDC1DN$"":DC0:DF0:NF0&DN$DN$DA$:56950:ˈDް56990:DN$"":200,30:"error":шuޱvޯ:DN$""56990}ޭNF1į180,30:"-"568501ݯ226,115239,125:P1226:P2115:56850Zݯ178,95191,105:P1178:P295:56850ݯ202,95215,105:P1202:P295:56850ݯ226,95239,105:P1226:P295:56850ԇݯ178,75191,85:P1178:P275:56850ݯ202,75215,85:P1202:P275:56850$N$,(DN$)1,1)" ":@DN$(DN$,(DN$)1):56990:56950:|ݰ55400:DN(DA$):DN56740,56750,56760,56770,56780,56790,56800,56810,56820:178,135191,145:P1178:P2135:56850ۆݯ178,115191,125:P1178:P2115:56850ݯ202,115215,125:P1202:P2115:C0ı ܭDC1DN$"":DC0:NF0>ܭDN$"0"DC0:NF0:DN$""cܰ56990:DF1:DN$DN$".":56950:ݰ55400:226,55239,65:P1226:P255:DC1ı"ݭ(DN$,1)"."DF0څ6ݭ(DN$)2DN$"0":NF0:DF0:56990:56950:;ݭDS1DN$(DN$,(DN$)2)"0"(DNF1DDDDܭDR1DNHNDD2ܭDR2DNHNDDEܭDR3DNHNDDXܭDR4DNHNDDsNF0:DN0NF1:DNDNܰ55250:DN(DN$):56990:DF0:DN(DN)DF1HNDN:NF1HNHN̈́ܰ56950:DR0:ܰ55400:202,135215,145:P1202:P2135:DF1D0:DR1:M۰55400:250,55263,65:P1250:P255:DP1:56430:DP0:DS0:DR3:۰55400:250,75263,85:P1250:P275:DP1:56430:DP0:DS0:DR4:Pܰ55400:250,135263,145:P1250:P2135nDC1:DR0HN(DN$):NF1HNHN:qܭDR0ı xDD(DN$):63,105:P1250:P295:DP1:56430:DP0:DS0:DR2:$۰55400:250,115263,125:P1250:P2115:DC1İ56990:NF1:DC0:DN$"0":56950:?ۭDN$"0"İ56990:NF1:56950:AۭDS1(DN$,2)"00"DN$(DN$,(DN$)3)"-00":56990:56950:BDP1:56430:DP0:DSО226,135239,145:P1226:P2135:DF0:NF1İ56900:qٰ56990:DN(DN$):DN(DN):55250:DN(DN$):DN(DN)DF1DN$(DN):56950:DC1:\ڰ55400:202,55215,65:P1202:P255zڰ56990:HN0:DR0:DS0:NF0:DF0:DN$"0":56950:0ڰ55400:250,952ذ55400:178,55191,65:P1178:P255:DC1ıO ٭DN$"0"DS1(DN$)1000ıuDS1:(DN$)DF3DN$(DN$,3DF)٭(DN$,1)"."DN$(DN$,(DN$)1)DN$DN$"E+00":56990:56950:DN$(DN$,(DN$)2)(DN$,1)DA$:56990:56950:2ٰ55400:$(DU):DU10DU$"0"DU$,DN$DN$DU$:P׭(DN$)8DN$(DN$,4)(DN$,4)Vرع216,0:(222)69(222)133(222)53ijد::DP1ġذ56900:DR0:NF0:DF0:DN$"":55050hحP10įP1,P2P113,P210:P10رد2:2:1::.9999999955270D~׭(DN$)8DN$(DN$,8):(DN$,1)"."DN$(DN$,7)x~DU0:DD1(DN$):(DN$,DD,1)"."DU(DN$)DD~ׂDD:DU4DN$(DN$,(DN$)DU4)~ױ~DU(DN$)1:DD1(DN$):(DN$,DD,1)"."DUDD1ׂDD:DN$(((DN$,3))100)"E+":DU}n׭DA$"X"DA$"*"İ56200/}x׭DA$"/"İ56300C}׭DA$"="İ56400W}׭DA$"."İ56500w}׭DA$(8)DA$(136)İ56600}׭(DA$)0(DA$)48(DA$)176İ56700}׫55100}DN$(DN):DS0:DD1(DN$):(DN$,DD,1)"E"DS1}ׂDD:DS155280~׭DNϯ1:1:0:165,25279,153:1:1:DF0:NF0:DC0:DP0:3::P10:P20:DN$"":55930a| ץ55300|<ׯDA$:DA$(27)DA$(155)55500|>׭DA$""İ57050|A׭DA$"E"İ55550|F׭DA$"R"İ55700|P׭DA$"C"İ55900|Z׭DA$"+"İ56000|d׭DA$"-"İ56100(JC4),Y1REJC(IC3){RE${={ MARK DRAWER X1.2O{X1,Y1X2,Y2{LN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LN{RE12.1LN1012{œX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3){꜂RE{U|֯:result from":"our mathematical analysis as":"we did from our graphical analysis."\zwi900nz@ MARK DRAWERzEX1,Y1X2,Y2zJLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNzTRE8LN810{^X1REIC(JC4),Y1REJC(IC3)X1REICne of .9195 ."(yBcAN$:AN$""25410FyLc57000:0:0,100279,191yVc0,100:" The cosine of 24 degrees is close":"to our calculated value."yc2:110,70:"=24|"yd(768)1Ĺ768,0:S29ye900ye 26Sze2:0,30:" We got the same 0,115:" Since vector a makes an angle of":"60| with the horizontal, the inside":"angle is 180|-60| = 120|.":1.5:121,80:"120|"jm800:0:0,117279,191jm1:X145:X2193:Y198:Y231:40000jm193,32185,28:193,32192,37km2:110,45:Y2100:40000Mim152,100146,95:152,100146,105:2:70,102:"b = 60 N"|im3:6:160,100180,100:190,100210,100im3:3:X1152:X2195:Y198:Y232:40000im195,32187,34:195,32197,38:2:167,83:"60|":180,59:"a = 40 N"jm2: The third way to find a":"resultant vector when the":"forces aren't acting at right":"angles is to use the law of":"cosines and the law of sines.":" Let's redraw the vectors":"head to tail."h_m900h`m 28 i~m3:3:3:X145:X2152:Y1100:,120279,191:3:2:990:gSNS1İ955:">RUN PRACTICE"[g1::3::::3:1igS0S24g0,0:WT$" "S;:W9,WY:1:0,18279,18:0,19279,19:3:2:.5gS1000g1:0,18279,18:0,19279,19:3ggxi 27hi2:0,30:""3fNI5SSESSFİ950:">RUN INSTRUCTIONS.E"`fNI6SSFİ950:">RUN INSTRUCTIONS.F"nfRR1956wf960fN$"#"(S)N$:N$f0:0,180WX,191:2:0,176:"Please wait...":HI:f0:110,0160,16:3f3:110,0:Sg0:0:S0SNS1ĺ::"There is not an "WT$" "S".":?eS0S24keNI1SSBİ950:">RUN INSTRUCTIONS.A"eNI2SSBSSCİ950:">RUN INSTRUCTIONS.B"eNI3SSCSSDİ950:">RUN INSTRUCTIONS.C"fNI4SSDSSEİ950:">RUN INSTRUCTIONS.DA$d>A$" "į:'dCA$" "İ55000:dEA$""İ57000ydHA$(1)į:D$"#"(S)N$: D$:HI:">RUN TEACHER.MENU"dRA$(2)SS(S0):910d\A$(0)820df:::5:"Which screen? ";WS$:(WS$)S(WS$)dp910d810:SS11eW10:49152)128Ă7c"?":10:I115:(49152)128Ă:755BcA$:Kc800c3:W1W11:WC(228):0:W9,0W920,15:228,WC:W9,0:(W196):2:c 810:WC(228):0:0,180WX,191:c*WW::2:0,176:"Press space bar";:WX,WY::d4:11,0:"?":10:11,0Qb750:A$(8)A$(13)A$" "(A$"0"A$"9")725ybA$(8)į11,0:10:N;:10:710bA$(13)A$" "NN10(A$):9:A$bb750:A$"0"A$"9"740bN(A$):N;:b:10 c"?":10:I120:(N$,2):(N$,1)"0"(N$,1)"9"1702aN$:910Na0:0,150279,191:3:YaF15iaX1,Y1:A$ra.3aX1,Y1:A$a.3::aA:AA64:A1A4700aa10:11,0:"?":10a750:A$"0"A$"9"715bN(A$):N;:9:103$!` "Instructions.E .`d:(21);`n115,HIG`x$9200`NS34:NI5:SB9:SC16:SD21:SE27:SF31:WW1:WT$"Instruction"`137`">BLOAD^START,A$9200"`$9200`N$`(N$,1)"#"S27:910`N$(N$,2):S(N$)$aN$(! ! !!!!!!!!!""" " " " " """""""""     S0SNB(NI2)NC(NI3)ND(NI4)NE(NI5):910T1:0,50279,50:0,51279,51g0,115279,115z0,116279,116毾20,60N$", this program"͌"will assist you in understanding"݌"vectors."9001":A$(A$,(A$)1)580202(A$)N58020lAAA1$"A"A1$"Z"A1$((A1$)32(AA1)):58140A1A1$"0"A1$"9"58140 AA$""58020ʋI11(AA$):A1$(AA$,I1,1)Ă:58020X((A$)),Y:A1$;&A$A$A1$:580203xNI120,46ޯAA$:2:2:1Xޯ:0:165,25279,153:1:1:3::56950:P10:P20^ ߱qA$"":49168,0{A1$A1$(13)A$""ıA1$(8)A1$(127)A$""58100͊X((A$)1),Yڊ(A$,1)X((A$)1),Y⯭(A$)1A$"]~DL(DN$):DD1DL:263DD9,30:(DN$,DL1DD,1)"."(DN$,DL1DD,1)"1"į265DD9,30y޺(DN$,DL1DD,1):DD:ޒ0:177,32264,46:ޱ޲ TRIG TABLEޯ1:1:20,46։ޯAA$:2:2:1:޲ TRIG TABLE FROM CALCޯ:1:ı#z ٭DN$"0"DS1(DN$)1000ıIzDS1:(DN$)DF3DN$(DN$,3DF)oz٭(DN$,1)"."DN$(DN$,(DN$)1)zDN$DN$"E+00":56990:56950:zDN$(DN$,(DN$)2)(DN$,1)DA$:56990:56950:{ٰ55400:226,135239,145:P1226:P2135:DF0:NF1İ5$y׭(DN$)8DN$(DN$,4)(DN$,4)*yرZyع216,0:(222)69(222)133(222)53ijkyد::DP1ġyذ56900:DR0:NF0:DF0:DN$"":55050yhحP10įP1,P2P113,P210:P10yرyد2:2:1::zذ55400:178,55191,65:P1178:P255:DC1(DN$,1)"."DN$(DN$,7)LxDU0:DD1(DN$):(DN$,DD,1)"."DU(DN$)DDqxׂDD:DU4DN$(DN$,(DN$)DU4)wxױxDU(DN$)1:DD1(DN$):(DN$,DD,1)"."DUDD1xׂDD:DN$(((DN$,3))100)"E+":DU$(DU):DU10DU$"0"DU$yDN$DN$DU$:300w׭DA$"="İ56400+w׭DA$"."İ56500Kw׭DA$(8)DA$(136)İ56600vw׭(DA$)0(DA$)48(DA$)176İ56700w׫55100wDN$(DN):DS0:DD1(DN$):(DN$,DD,1)"E"DS1wׂDD:DS155280w׭DN9999999955270x׭(DN$)8DN$(DN$,8):0:DC0:DP0:3::P10:P20:DN$"":559305v ץ55300[v<ׯDA$:DA$(27)DA$(155)55500ov>׭DA$""İ57050vA׭DA$"E"İ55550vF׭DA$"R"İ55700vP׭DA$"C"İ55900vZ׭DA$"+"İ56000vd׭DA$"-"İ56100vn׭DA$"X"DA$"*"İ56200wx׭DA$"/"İ56 MARK DRAWER X1.2#uX1,Y1X2,Y2auLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNwuRE12.1LN1012uœX1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)u꜂REu)v֯:1:1:0:165,25279,153:1:1:DF0:NF,1:900%tvuAN$"1"S20:768,1:900.ty900@t@ MARK DRAWERRtEX1,Y1X2,Y2tJLN(((X1X2)2)((Y1Y2)2)):IC(X2X1)LN:JC(Y2Y1)LNtTRE17LN1518t^X1REIC(JC4),Y1REJC(IC3)X1REIC(JC4),Y1REJC(IC3)tREtu s?u"appropriate key."sDu1,124:"1. Graphical method":0,137:"2. Component parts method":"3. Law of cosines and sines method":"4. Continue the lesson"sNuAN$:AN$"4"AN$"1"30030sXuAN$"4"ī900sbuAN$"3"S26:900tluAN$"2"S22:76824 degrees.":83,82:"24|"$r/u900.r0u 30r:u2:0,30:" We have seen three ways to":"calculate the resultant force":"vector when two forces are"r