{VERSION 7 0 "Windows XP" "7.0" } {USTYLETAB {PSTYLE "Ordered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 } {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "MS Serif" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output " -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 3 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "MS S erif" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 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Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 201 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "MS Serif" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Type setting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi(\"restart\"), Typ esetting:-mo(\":\", form = \"infix\", fence = \"false\", separator = \+ \"false\", lspace = \"thickmathspace\", rspace = \"thickmathspace\", s tretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", mi nsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent \+ = \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mo(\"&In visibleTimes;\", form = \"infix\", fence = \"false\", separator = \"fa lse\", lspace = \"thickmathspace\", rspace = \"thickmathspace\", stret chy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsiz e = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", font_style_name = \"2D Input\", size = \"12\", foreground = \+ \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"with\" ), Typesetting:-mo(\"⁡\", form = \"infix\", fence = \"fa lse\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stre tchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsi ze = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", font_style_name = \"2D Input\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mfenced(Ty pesetting:-mrow(Typesetting:-mi(\"DEtools\"))), Typesetting:-mi(\"\")) , Typesetting:-mo(\":\", form = \"infix\", fence = \"false\", separato r = \"false\", lspace = \"thickmathspace\", rspace = \"thickmathspace \", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity \", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", font_style_name = \"2D Input\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi (\"\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typeset tingGI(_syslibGF'6'-I#miGF$6#Q!F'-F#6)-F,6#Q(restartF'-I#moGF$63Q\":F' /%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF=/%'lspaceGQ/thickmat hspaceF'/%'rspaceGFB/%)stretchyGF=/%*symmetricGF=/%(maxsizeGQ)infinity F'/%(minsizeGQ\"1F'/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%0font _style_nameGQ)2D~InputF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+back groundGQ.[255,255,255]F'-F563Q1⁢F'F8F;F>F@FCFEFGFIFLFOF QFSFUFXFenFhn-F,6#Q%withF'-F563Q0⁡F'F8F;F>/FAQ$0emF'/FDF eoFEFGFIFLFOFQFSFUFXFenFhn-I(mfencedGF$6#-F#6#-F,6#Q(DEtoolsF'F+F4F+F+ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 23 "Section 2.3 Problem #22" }} {PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 17 "A ball \+ with mass " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"m\"), T ypesetting:-mo(\"⁢\", form = \"infix\", fence = \"false \", separator = \"false\", lspace = \"thickmathspace\", rspace = \"thi ckmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \+ \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", font_style_name = \"2D Math\", size = \"1 2\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"));" "-I% mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6$-I#miGF$6#Q\"mF'-I #moGF$63Q1⁢F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*sepa ratorGF8/%'lspaceGQ/thickmathspaceF'/%'rspaceGF=/%)stretchyGF8/%*symme tricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/%(largeopGF8/%.movable limitsGF8/%'accentGF8/%0font_style_nameGQ(2D~MathF'/%%sizeGQ#12F'/%+fo regroundGQ([0,0,0]F'/%+backgroundGQ.[255,255,255]F'" }{TEXT 200 50 "(i n kilograms) is thrown up with initial velocity " }{XPPEDIT 2 0 "Types etting:-mrow(Typesetting:-mi(\"\"), Typesetting:-msub(Typesetting:-mi( \"v\"), Typesetting:-mn(\"0\"), subscriptshift = \"0\", placeholder = \+ \"false\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typ esettingGI(_syslibGF'6%-I#miGF$6#Q!F'-I%msubGF$6&-F,6#Q\"vF'-I#mnGF$6# Q\"0F'/%/subscriptshiftGQ\"0F'/%,placeholderGQ&falseF'F+" }{TEXT 200 41 " (in meters per second) from a height of " }{XPPEDIT 2 0 "Typesett ing:-mrow(Typesetting:-mi(\"\"), Typesetting:-msub(Typesetting:-mi(\"x \"), Typesetting:-mn(\"0\"), subscriptshift = \"0\", placeholder = \"f alse\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typese ttingGI(_syslibGF'6%-I#miGF$6#Q!F'-I%msubGF$6&-F,6#Q\"xF'-I#mnGF$6#Q\" 0F'/%/subscriptshiftGQ\"0F'/%,placeholderGQ&falseF'F+" }{TEXT 200 32 " (meters). The force due to air " }}{PARA 0 "" 0 "" {TEXT 200 14 "resi stance is " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"mu\"), \+ Typesetting:-mo(\"⋅\", form = \"infix\", fence = \"false\", separ ator = \"false\", lspace = \"thickmathspace\", rspace = \"thickmathspa ce\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinit y\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", font_style_name = \"2D Math\", size = \"12\", fore ground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-ms up(Typesetting:-mi(\"v\"), Typesetting:-mn(\"2\"), superscriptshift = \+ \"0\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typeset tingGI(_syslibGF'6&-I#miGF$6#Q#muF'-I#moGF$63Q'⋅F'/%%formGQ&infix F'/%&fenceGQ&falseF'/%*separatorGF8/%'lspaceGQ/thickmathspaceF'/%'rspa ceGF=/%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ \"1F'/%(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_nameGQ( 2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,2 55,255]F'-I%msupGF$6%-F,6#Q\"vF'-I#mnGF$6#Q\"2F'/%1superscriptshiftGQ \"0F'-F,6#Q!F'" }{TEXT 200 2 " (" }{XPPEDIT 2 0 "Typesetting:-mrow(Typ esetting:-mi(\"mu\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_s yslibGF'6#-I#miGF$6#Q#muF'" }{TEXT 200 33 " is a fixed drag constant) \+ where " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), Typese tting:-mrow(Typesetting:-mi(\"v\"), Typesetting:-mo(\"⁡ \", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric = \"fals e\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", mov ablelimits = \"false\", accent = \"false\", font_style_name = \"2D Mat h\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255, 255]\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"t\") ))), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typesettin gGI(_syslibGF'6%-I#miGF$6#Q!F'-F#6%-F,6#Q\"vF'-I#moGF$63Q0&ApplyFuncti on;F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF=/%'lspaceGQ$0em F'/%'rspaceGFB/%)stretchyGF=/%*symmetricGF=/%(maxsizeGQ)infinityF'/%(m insizeGQ\"1F'/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%0font_style _nameGQ(2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundG Q.[255,255,255]F'-I(mfencedGF$6#-F#6#-F,6#Q\"tF'F+" }{TEXT 200 57 "is \+ the velocity (in meters per second) of the ball after " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"t\"));" "-I%mrowG6#/I+modulenameG 6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6#Q\"tF'" }{TEXT 200 30 " secon ds. We will make \"up\" " }}{PARA 0 "" 0 "" {TEXT 200 74 "positive and \"down\" negative. We will call the height of the ball after " } {XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"t\"));" "-I%mrowG6#/ I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6#Q\"tF'" }{TEXT 200 9 " seconds " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\" \"), Typesetting:-mrow(Typesetting:-mi(\"x\"), Typesetting:-mo(\"&Appl yFunction;\", form = \"infix\", fence = \"false\", separator = \"false \", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetri c = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", font_style_name \+ = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", background = \+ \"[255,255,255]\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting :-mi(\"t\")))), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I ,TypesettingGI(_syslibGF'6%-I#miGF$6#Q!F'-F#6%-F,6#Q\"xF'-I#moGF$63Q0& ApplyFunction;F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF=/%'l spaceGQ$0emF'/%'rspaceGFB/%)stretchyGF=/%*symmetricGF=/%(maxsizeGQ)inf inityF'/%(minsizeGQ\"1F'/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/% 0font_style_nameGQ(2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+ backgroundGQ.[255,255,255]F'-I(mfencedGF$6#-F#6#-F,6#Q\"tF'F+" }{TEXT 200 13 " (in meters)." }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 17 "Remembering that " }{XPPEDIT 2 0 "Typesetting:-mrow( Typesetting:-mi(\"F\"), Typesetting:-mo(\"=\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"thickmathspace\", rspa ce = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", \+ maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablel imits = \"false\", accent = \"false\", font_style_name = \"2D Math\", \+ size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255] \"), Typesetting:-mi(\"ma\"));" "-I%mrowG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6%-I#miGF$6#Q\"FF'-I#moGF$63Q\"=F'/%%formGQ&infixF'/%& fenceGQ&falseF'/%*separatorGF8/%'lspaceGQ/thickmathspaceF'/%'rspaceGF= /%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/ %(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_nameGQ(2D~Mat hF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,255,255 ]F'-F,6#Q#maF'" }{TEXT 200 10 " and that " }{XPPEDIT 2 0 "Typesetting: -mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi(\"a\"), Typesetting:-mo(\"⁡\", form = \"infix\", fence = \"fals e\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretc hy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"f alse\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[ 0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mfenced(Typese tting:-mrow(Typesetting:-mi(\"t\")))), Typesetting:-mo(\"=\", form = \+ \"infix\", fence = \"false\", separator = \"false\", lspace = \"thickm athspace\", rspace = \"thickmathspace\", stretchy = \"false\", symmetr ic = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"f alse\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", background = \+ \"[255,255,255]\"), Typesetting:-mrow(Typesetting:-mi(\"diff\"), Types etting:-mo(\"⁡\", form = \"infix\", fence = \"false\", s eparator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \+ \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \" 1\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0, 0]\", background = \"[255,255,255]\"), Typesetting:-mfenced(Typesettin g:-mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi(\"v\" ), Typesetting:-mo(\"⁡\", form = \"infix\", fence = \"fa lse\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stre tchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsi ze = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", font_style_name = \"2D Math\", size = \"12\", foreground = \+ \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mfenced(Typ esetting:-mrow(Typesetting:-mi(\"t\")))), Typesetting:-mo(\",\", form \+ = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\" , rspace = \"verythickmathspace\", stretchy = \"false\", symmetric = \+ \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false \", movablelimits = \"false\", accent = \"false\", font_style_name = \+ \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", background = \"[ 255,255,255]\"), Typesetting:-mi(\"t\")))), Typesetting:-mi(\"\"));" " -I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I#miGF$6#Q!F'- F#6%-F,6#Q\"aF'-I#moGF$63Q0⁡F'/%%formGQ&infixF'/%&fenceG Q&falseF'/%*separatorGF=/%'lspaceGQ$0emF'/%'rspaceGFB/%)stretchyGF=/%* symmetricGF=/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/%(largeopGF=/%.mo vablelimitsGF=/%'accentGF=/%0font_style_nameGQ(2D~MathF'/%%sizeGQ#12F' /%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,255,255]F'-I(mfencedGF$6 #-F#6#-F,6#Q\"tF'-F563Q\"=F'F8F;F>/FAQ/thickmathspaceF'/FDFgoFEFGFIFLF OFQFSFUFXFenFhn-F#6%-F,6#Q%diffF'F4-F\\o6#-F#6&F+-F#6%-F,6#Q\"vF'F4F[o -F563Q\",F'F8F;/F?Q%trueF'F@/FDQ3verythickmathspaceF'FEFGFIFLFOFQFSFUF XFenFhnF`oF+" }{TEXT 200 46 ", we get the following differential equat ion (" }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"g\"));" "-I% mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6#Q\"gF'" }{TEXT 200 37 " is the acceleration due to gravity):" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "UPEquation := m*(diff(v(t), t)) = -mu*v(t)^ 2-m*g; 1;" "C$>I+UPEquationG6\"/*&I\"mGF%\"\"\"-I%diffG%*protectedG6$- I\"vGF%6#I\"tGF%F1F),&*&I#muGF%F))F.\"\"#F)!\"\"*&F(F)I\"gGF%F)F7F)" } }{PARA 11 "" 1 "" {XPPMATH 20 ">I+UPEquationG6\"/*&I\"mGF$\"\"\"-I%dif fG%*protectedG6$-I\"vGF$6#I\"tGF$F0F(,&*&I#muGF$F()F-\"\"#F(!\"\"*&F'F (I\"gGF$F(F6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 125 "Both gravity an d air resistance slow the ball down on the trip upwards (both pull \"d own\"), so both forces get a minus sign." }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 123 "On the way down, gravity speeds \+ up the ball while air resistance slows the ball down. Gravity gets a m inus sign (since it's" }}{PARA 0 "" 0 "" {TEXT 200 102 "still pulling \+ \"down\") while air resistance gets a plus sign (since it's now sort o f pulling \"up\")." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "DOWNEqu ation := m*(diff(v(t), t)) = mu*v(t)^2-m*g; 1;" "C$>I-DOWNEquationG6\" /*&I\"mGF%\"\"\"-I%diffG%*protectedG6$-I\"vGF%6#I\"tGF%F1F),&*&I#muGF% F))F.\"\"#F)F)*&F(F)I\"gGF%F)!\"\"F)" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I-DOWNEquationG6\"/*&I\"mGF$\"\"\"-I%diffG%*protectedG6$-I\"vGF$6#I\" tGF$F0F(,&*&I#muGF$F()F-\"\"#F(F(*&F'F(I\"gGF$F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 102 "We solve the differential equation gove rning the upward motion of the ball given the initial velocity " } {XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-mr ow(Typesetting:-mi(\"v\"), Typesetting:-mo(\"⁡\", form = \"infix\", fence = \"false\", separator = \"false\", lspace = \"0em\" , rspace = \"0em\", stretchy = \"false\", symmetric = \"false\", maxsi ze = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Math\", size \+ = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), T ypesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(\"0\")))), Types etting:-mo(\"=\", form = \"infix\", fence = \"false\", separator = \"f alse\", lspace = \"thickmathspace\", rspace = \"thickmathspace\", stre tchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsi ze = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", font_style_name = \"2D Math\", size = \"12\", foreground = \+ \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-msub(Typese tting:-mi(\"v\"), Typesetting:-mn(\"0\"), subscriptshift = \"0\", plac eholder = \"false\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenam eG6\"I,TypesettingGI(_syslibGF'6'-I#miGF$6#Q!F'-F#6%-F,6#Q\"vF'-I#moGF $63Q0⁡F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorG F=/%'lspaceGQ$0emF'/%'rspaceGFB/%)stretchyGF=/%*symmetricGF=/%(maxsize GQ)infinityF'/%(minsizeGQ\"1F'/%(largeopGF=/%.movablelimitsGF=/%'accen tGF=/%0font_style_nameGQ(2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0 ]F'/%+backgroundGQ.[255,255,255]F'-I(mfencedGF$6#-F#6#-I#mnGF$6#Q\"0F' -F563Q\"=F'F8F;F>/FAQ/thickmathspaceF'/FDFhoFEFGFIFLFOFQFSFUFXFenFhn-I %msubGF$6&F1F`o/%/subscriptshiftGQ\"0F'/%,placeholderGF=F+" }{TEXT 200 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "UpVELOCITY := sim plify(dsolve(\{UPEquation, v(0) = v[0]\})); 1;" "C$>I+UpVELOCITYG6\"-I )simplifyGF%6#-I'dsolveGF%6#<$I+UPEquationGF%/-I\"vGF%6#\"\"!&F0F1\"\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+UpVELOCITYG6\"/-I\"vGF$6#I\"tGF $,$*(-I$tanG6$%*protectedGI(_syslibGF$6#*&,&*&F)\"\"\")*(I\"mGF$F5I\"g GF$F5I#muGF$F5#F5\"\"#F5F5*&F8F5-I'arctanGF.6#*(F:F5&F'6#\"\"!F5F6!\" \"F5FEF5F8FEF5F6F5F:FEFE" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 108 "Now that we know the velocity, we can integrate and find the position fun ction. However, we must remember to" }}{PARA 0 "" 0 "" {TEXT 200 29 "p lug in the initial position " }{XPPEDIT 2 0 "Typesetting:-mrow(Typeset ting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi(\"x\"), Typesetting: -mo(\"⁡\", form = \"infix\", fence = \"false\", separato r = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false \", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font _style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", ba ckground = \"[255,255,255]\"), Typesetting:-mfenced(Typesetting:-mrow( Typesetting:-mn(\"0\")))), Typesetting:-mo(\"=\", form = \"infix\", fe nce = \"false\", separator = \"false\", lspace = \"thickmathspace\", r space = \"thickmathspace\", stretchy = \"false\", symmetric = \"false \", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", font_style_name = \"2D Math \", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,2 55]\"), Typesetting:-msub(Typesetting:-mi(\"x\"), Typesetting:-mn(\"0 \"), subscriptshift = \"0\", placeholder = \"false\"), Typesetting:-mi (\"\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I#m iGF$6#Q!F'-F#6%-F,6#Q\"xF'-I#moGF$63Q0⁡F'/%%formGQ&infix F'/%&fenceGQ&falseF'/%*separatorGF=/%'lspaceGQ$0emF'/%'rspaceGFB/%)str etchyGF=/%*symmetricGF=/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/%(larg eopGF=/%.movablelimitsGF=/%'accentGF=/%0font_style_nameGQ(2D~MathF'/%% sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,255,255]F'-I( mfencedGF$6#-F#6#-I#mnGF$6#Q\"0F'-F563Q\"=F'F8F;F>/FAQ/thickmathspaceF '/FDFhoFEFGFIFLFOFQFSFUFXFenFhn-I%msubGF$6&F1F`o/%/subscriptshiftGQ\"0 F'/%,placeholderGF=F+" }{TEXT 200 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "UpPOSITION := simplify(dsolve(\{diff(x(t), t) = rhs(UpV ELOCITY), x(0) = x[0]\})); 1;" "C$>I+UpPOSITIONG6\"-I)simplifyG6$%*pro tectedGI(_syslibGF%6#-I'dsolveGF(6#<$/-I%diffGF)6$-I\"xGF%6#I\"tGF%F7- I$rhsGF)6#I+UpVELOCITYGF%/-F56#\"\"!&F5F>\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+UpPOSITIONG6\"/-I\"xGF$6#I\"tGF$,$*(#\"\"\"\"\"#F-,**( F.F-I\"mGF$F--I#lnG6$%*protectedGI(_syslibGF$6#,&*$)*(F1F-I\"gGF$F-I#m uGF$F-F,F-F-*(-I$tanGF46#*(F1!\"\"F)F-F:F-F-F=F-&I\"vGF$6#\"\"!F-F-F-F -*&F1F--F36#,&F-F-*$)F?F.F-F-F-FC*(F.F-&F'FFF-F=F-F-*&F1F--F36#F;F-FCF -F=FCF-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 101 "The ball achieves it s maximum height when its velocity vanishes (becomes zero). Solving th e equation " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"\"), T ypesetting:-mrow(Typesetting:-mi(\"v\"), Typesetting:-mo(\"&ApplyFunct ion;\", form = \"infix\", fence = \"false\", separator = \"false\", ls pace = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric = \" false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255, 255,255]\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\" t\")))), Typesetting:-mo(\"=\", form = \"infix\", fence = \"false\", s eparator = \"false\", lspace = \"thickmathspace\", rspace = \"thickmat hspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"inf inity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", font_style_name = \"2D Math\", size = \"12\", \+ foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting :-mn(\"0\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 &-I#miGF$6#Q!F'-F#6%-F,6#Q\"vF'-I#moGF$63Q0⁡F'/%%formGQ& infixF'/%&fenceGQ&falseF'/%*separatorGF=/%'lspaceGQ$0emF'/%'rspaceGFB/ %)stretchyGF=/%*symmetricGF=/%(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/% (largeopGF=/%.movablelimitsGF=/%'accentGF=/%0font_style_nameGQ(2D~Math F'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,255,255] F'-I(mfencedGF$6#-F#6#-F,6#Q\"tF'-F563Q\"=F'F8F;F>/FAQ/thickmathspaceF '/FDFgoFEFGFIFLFOFQFSFUFXFenFhn-I#mnGF$6#Q\"0F'" }{TEXT 200 5 " for " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"t\"));" "-I%mrowG6# /I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#miGF$6#Q\"tF'" }{TEXT 200 8 ", gives " }}{PARA 0 "" 0 "" {TEXT 200 53 "us the time when the \+ ball reaches its maximum height." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "HighTime := solve(rhs(UpVELOCITY) = 0, t); 1;" "C$>I)Hi ghTimeG6\"-I&solveG6$%*protectedGI(_syslibGF%6$/-I$rhsGF)6#I+UpVELOCIT YGF%\"\"!I\"tGF%\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)HighTimeG6 \"*(I\"mGF$\"\"\"-I'arctanG6$%*protectedGI(_syslibGF$6#*(I#muGF$F'&I\" vGF$6#\"\"!F')*(F&F'I\"gGF$F'F/F'#F'\"\"#!\"\"F'F4F9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 130 "If we plug in the time when the ball reached \+ its maximum height into the position function, we will get the ball's \+ maximum height." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "HighestPos ition := simplify(subs(t = HighTime, rhs(UpPOSITION))); 1;" "C$>I0High estPositionG6\"-I)simplifyG6$%*protectedGI(_syslibGF%6#-I%subsGF)6$/I \"tGF%I)HighTimeGF%-I$rhsGF)6#I+UpPOSITIONGF%\"\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 ">I0HighestPositionG6\",$*(#\"\"\"\"\"#F(,**(F)F(I\"mGF$ F(-I#lnG6$%*protectedGI(_syslibGF$6#*(I#muGF$F(,&*&F,F(I\"gGF$F(F(*&)& I\"vGF$6#\"\"!F)F(F4F(F(F()*(F,F(F7F(F4F(F'!\"\"F(F(*&F,F(-F.6#*(F5F(F ,F@F7F@F(F@*(F)F(&I\"xGF$F " 0 "" {XPPEDIT 19 1 "DownVELOCITY := simpl ify(dsolve(\{DOWNEquation, v(HighTime) = 0\})); 1;" "C$>I-DownVELOCITY G6\"-I)simplifyG6$%*protectedGI(_syslibGF%6#-I'dsolveGF(6#<$I-DOWNEqua tionGF%/-I\"vGF%6#I)HighTimeGF%\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-DownVELOCITYG6\"/-I\"vGF$6#I\"tGF$,$*(-I%tanhG6$%*prot ectedGI(_syslibGF$6#*&,&*&F)\"\"\")*(I\"mGF$F5I\"gGF$F5I#muGF$F5#F5\" \"#F5F5*&F8F5-I'arctanGF.6#*(F:F5&F'6#\"\"!F5F6!\"\"F5FEF5F8FEF5F6F5F: FEFE" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 126 "If we integrate the (do wnward) velocity function remembering to start at the highest position at the time the ball reached its" }}{PARA 0 "" 0 "" {TEXT 200 88 "hig hest position, we will have the position function of the ball as it tr avels downward." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "DownPOSITI ON := simplify(dsolve(\{diff(x(t), t) = rhs(DownVELOCITY), x(HighTime) = HighestPosition\})); 1;" "C$>I-DownPOSITIONG6\"-I)simplifyG6$%*prot ectedGI(_syslibGF%6#-I'dsolveGF(6#<$/-I%diffGF)6$-I\"xGF%6#I\"tGF%F7-I $rhsGF)6#I-DownVELOCITYGF%/-F56#I)HighTimeGF%I0HighestPositionGF%\"\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-DownPOSITIONG6\"/-I\"xGF$6#I\"t GF$,$*(#\"\"\"\"\"#F-,,*(F.F-I\"mGF$F--I#lnG6$%*protectedGI(_syslibGF$ 6#-I%coshGF46#*&,&*&F)F-)*(F1F-I\"gGF$F-I#muGF$F-F,F-F-*&F1F--I'arctan GF46#*(FAF-&I\"vGF$6#\"\"!F-F>!\"\"F-FKF-F1FKF-FK*(F.F-F1F--F36#*(FAF- ,&*&F1F-F@F-F-*&)FGF.F-FAF-F-F-F>FKF-F-*&F1F--F36#*(FPF-F1FKF@FKF-FK*( F.F-&F'FIF-FAF-F-*&F1F--F36#F?F-FKF-FAFKF-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 96 "When the ball's downward position reaches zero, it has h it the ground. So we solve the equation " }{XPPEDIT 2 0 "Typesetting:- mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi(\"x\"), \+ Typesetting:-mo(\"⁡\", form = \"infix\", fence = \"false \", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretch y = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize \+ = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0 ,0,0]\", background = \"[255,255,255]\"), Typesetting:-mfenced(Typeset ting:-mrow(Typesetting:-mi(\"t\")))), Typesetting:-mo(\"=\", form = \" infix\", fence = \"false\", separator = \"false\", lspace = \"thickmat hspace\", rspace = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"fal se\", movablelimits = \"false\", accent = \"false\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", background = \" [255,255,255]\"), Typesetting:-mn(\"0\"));" "-I%mrowG6#/I+modulenameG6 \"I,TypesettingGI(_syslibGF'6&-I#miGF$6#Q!F'-F#6%-F,6#Q\"xF'-I#moGF$63 Q0⁡F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF=/ %'lspaceGQ$0emF'/%'rspaceGFB/%)stretchyGF=/%*symmetricGF=/%(maxsizeGQ) infinityF'/%(minsizeGQ\"1F'/%(largeopGF=/%.movablelimitsGF=/%'accentGF =/%0font_style_nameGQ(2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F' /%+backgroundGQ.[255,255,255]F'-I(mfencedGF$6#-F#6#-F,6#Q\"tF'-F563Q\" =F'F8F;F>/FAQ/thickmathspaceF'/FDFgoFEFGFIFLFOFQFSFUFXFenFhn-I#mnGF$6# Q\"0F'" }{TEXT 200 5 " for " }{XPPEDIT 2 0 "Typesetting:-mrow(Typesett ing:-mi(\"t\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6#-I#miGF$6#Q\"tF'" }{TEXT 200 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "HitsGround := solve(rhs(DownPOSITION) = 0, t); 1;" "C$> I+HitsGroundG6\"-I&solveG6$%*protectedGI(_syslibGF%6$/-I$rhsGF)6#I-Dow nPOSITIONGF%\"\"!I\"tGF%\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+Hit sGroundG6\"*(I\"mGF$\"\"\",&-I'arctanG6$%*protectedGI(_syslibGF$6#*(I# muGF$F'&I\"vGF$6#\"\"!F')*(F&F'I\"gGF$F'F0F'#F'\"\"#!\"\"F'-I(arccoshG F+6#-I$expGF+6#,$*(F8F',**(F9F'F&F'-I#lnGF+6#*&F0F',&*&F&F'F7F'F'*&)F1 F9F'F0F'F'F'F'F'*(F9F'F&F'-FF6#F6F'F:*&F&F'-FF6#*(FIF'F&F:F7F:F'F:*(F9 F'&I\"xGF$F3F'F0F'F'F'F&F:F'F'F'F5F:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 68 "The problem in the book provides the following specific inform ation:" }}{PARA 0 "" 0 "" {TEXT 200 51 "The initial position is 30 met ers above the ground." }}{PARA 0 "" 0 "" {TEXT 200 60 "The ball is thr own upward at a rate of 20 meters per second." }}{PARA 0 "" 0 "" {TEXT 200 21 "The drag constant is " }{XPPEDIT 2 0 "Typesetting:-mrow(Types etting:-mi(\"mu\"), Typesetting:-mo(\"=\", form = \"infix\", fence = \+ \"false\", separator = \"false\", lspace = \"thickmathspace\", rspace \+ = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", max size = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimi ts = \"false\", accent = \"false\", font_style_name = \"2D Math\", siz e = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mfrac(Typesetting:-mn(\"1\"), Typesetting:-mn(\"1325\"), linethickness = \"1\", denomalign = \"center\", numalign = \"center\" , bevelled = \"false\", foreground = \"[0,0,0]\", background = \"[255, 255,255]\"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Ty pesettingGI(_syslibGF'6&-I#miGF$6#Q#muF'-I#moGF$63Q\"=F'/%%formGQ&infi xF'/%&fenceGQ&falseF'/%*separatorGF8/%'lspaceGQ/thickmathspaceF'/%'rsp aceGF=/%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(minsizeGQ \"1F'/%(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_nameGQ( 2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ.[255,2 55,255]F'-I&mfracGF$6*-I#mnGF$6#FI-Fjn6#Q%1325F'/%.linethicknessGQ\"1F '/%+denomalignGQ'centerF'/%)numalignGFdo/%)bevelledGF8FVFY-F,6#Q!F'" } {TEXT 200 1 "." }}{PARA 0 "" 0 "" {TEXT 200 19 "The ball's mass is " } {XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mn(\"0.15\"));" "-I%mrowG 6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6#-I#mnGF$6#Q%0.15F'" } {TEXT 200 11 " kilograms." }}{PARA 0 "" 0 "" {TEXT 200 88 "(And of cou rse the acceleration due to gravity is about 9.81 meters per second sq uared.)" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "x[0] := 30; 1; v[0 ] := 20; 1; mu := 1/1325; 1; m := .15; 1; g := 9.81; 1;" "C,>&I\"xG6\" 6#\"\"!\"#I\"\"\">&I\"vGF&F'\"#?F*>I#muGF&#F*\"%D8F*>I\"mGF&$\"#:!\"#F *>I\"gGF&$\"$\")*F7F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"xG6\"6#\" \"!\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"vG6\"6#\"\"!\"#?" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I#muG6\"#\"\"\"\"%D8" }}{PARA 11 "" 1 " " {XPPMATH 20 ">I\"mG6\"$\"#:!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I \"gG6\"$\"$\")*!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 117 "We creat e a plot of the upward velocity function from time 0 until the time wh en the ball reached its maximal height." }}{PARA 0 "" 0 "" {TEXT 200 138 "Then we create a plot of the downward velocity function from the \+ time of the ball's maximal height until the time when it hits the grou nd." }}{PARA 0 "" 0 "" {TEXT 200 40 "Finally, we display both plots to gether." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "VUp := plot(rhs(Up VELOCITY), t = 0 .. HighTime); 1; VDown := plot(rhs(DownVELOCITY), t = HighTime .. HitsGround); 1; plots[display](VUp, VDown); 1;" "C(>I$VUp G6\"-I%plotG6$%*protectedGI(_syslibGF%6$-I$rhsGF)6#I+UpVELOCITYGF%/I\" tGF%;\"\"!I)HighTimeGF%\"\"\">I&VDownGF%-F'6$-F-6#I-DownVELOCITYGF%/F1 ;F4I+HitsGroundGF%F5-&I&plotsGF(6#I(displayGF%6$F$F7F5" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$VUpG6\"-I/INTERFACE_PLOTGF$6%-I'CURVESG6$%*protec tedGI(_syslibGF$6$7S7$$\"\"!F1$\"3y!#;7$$\"3?'f&Q*oWE<%!# >$\"3ycE^\\M(3&>F47$$\"3r)35E_SK!yF8$\"3)Q4JCCb%3>F47$$\"3'3dB\\_A')= \"!#=$\"3Oim:@K5h=F47$$\"3!o:**[YF'*f\"FC$\"31#HXIg,Q\"=F47$$\"3$y0C'*)RhnFC$\"3'Q/L)HdBY7F47$$\"37h/!\\aCl=(FC$\"3aFx)R?F8?\"F47 $$\"3_jog?F$Gc(FC$\"3-UzxOzwh6F47$$\"3],U*4V-d(zFC$\"3o(*Rf(ok&=6F47$$ \"3gFWYI?&)o$)FC$\"3W-*4))H6w2\"F47$$\"3q!G5MRi!z()FC$\"3LgwXaj1N5F47$ $\"3KL4TgNwb\"*FC$\"3_ySdjych**!#<7$$\"3oK6efm3i&*FC$\"3TQ_\"3$y^V&*Fd s7$$\"3gXBfk@9%)**FC$\"30]ir?U+6\"*Fds7$$\"34!HTAFa^.\"Fds$\"33zZ\"Q#G 'et)Fds7$$\"3QGE,RX$[2\"Fds$\"3tN9&H%p0K$)Fds7$$\"3==VIP\"Ge6\"Fds$\"3 FUlPMPH;zFds7$$\"37d&QcPKf:\"Fds$\"3\")G:P9G'3^(Fds7$$\"3K[%[$)GNZ>\"F ds$\"3?w`+siv>rFds7$$\"3Hss>2$>yB\"Fds$\"3e?b/n&ono'Fds7$$\"3'44sV@KlF \"Fds$\"3-p&f&f9y)H'Fds7$$\"38'z&)e]myJ\"Fds$\"37^tE\\0d&)eFds7$$\"3[z 3[<:Kb8Fds$\"30l!*3(f9?^&Fds7$$\"3y+$>$Q(piR\"Fds$\"3t%)RQhW]/^Fds7$$ \"3-%yeH#))zM9Fds$\"3fzw;9B&=s%Fds7$$\"3sc\"e!=G2v9Fds$\"3,R!*[.yhAVFd s7$$\"3#[)Qo4![W^\"Fds$\"3@5x>]\"pH$RFds7$$\"3w'=8i=qcb\"Fds$\"3>G5&H@ #pDNFds7$$\"3K+GeT?P&f\"Fds$\"3tK.wE'**R8$Fds7$$\"3ndU'H#H(fj\"Fds$\"3 d-ww7Q%Rt#Fds7$$\"3)Q$*[&3wBw;Fds$\"3%z6r'H>kPBFds7$$\"3#fxsGnOKr\"Fds $\"3?l$yV'R\"Q(>Fds7$$\"39m,$fxTcv\"Fds$\"3k,TO6=:d:Fds7$$\"3?*f>cSpNz \"Fds$\"3mkgr14s%=\"Fds7$$\"3?yw^p\"3S$=Fds$\"3=(y,9^g\"yyFC7$$\"3UZ\" QkA8F(=Fds$\"3cto(=zu/3%FC7$$\"3$******f42V\">Fds$\"3V&=C0*o;/S!#E-I'C OLOURGF*6&I$RGBGF*$\"#5!\"\"F0F0-I+AXESLABELSGF*6$Q\"tF$Q!F$-I%VIEWGF* 6$;F0$\"+'42V\">!\"*I(DEFAULTGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&V DownG6\"-I/INTERFACE_PLOTGF$6%-I'CURVESG6$%*protectedGI(_syslibGF$6$7S 7$$\"3$******f42V\">!#<$\"3V&=C0*o;/S!#E7$$\"3sw9X+?q&)>F2$!3$o-%yvFD. q!#=7$$\"3gE#o]KAy/#F2$!3nP:8x.S48F27$$\"3f(phq7$o<@F2$!3Q()\\R_Aw$*>F 27$$\"3u$3*z6q+)=#F2$!3OWC9wv+R#F2$!3O*)Q9x0)*\\YF2 7$$\"3Gog%3Mi&fCF2$!3-n#>eJUHK&F27$$\"3rJj4Pm#)GDF2$!3Mp<3n#e7*fF27$$ \"3H^RXzM2+EF2$!3a>Gp?\\zvmF27$$\"3+3I)ptFGm#F2$!3m!)*=9_QgF(F27$$\"3J a_lnTZLFF2$!39Xct2xY[zF27$$\"3N5%f$z1T/GF2$!3@F2!zaX)>')F27$$\"31YBg_6 xsGF2$!3qC3wD%\\HE*F27$$\"3C3tN6!\\[$HF2$!3l_P[8uTV)*F27$$\"3G2gr*el'3 IF2$!3+I4cu.!H0\"!#;7$$\"3a\\B79z>rIF2$!3GUTp%*=c56Faq7$$\"3jX!eJ(y$R9 $F2$!3oje]R&Hr<\"Faq7$$\"3Epj@i]K3KF2$!3kUF&zexbB\"Faq7$$\"3#f%QV8!o*y KF2$!3#p2x-cn\"*H\"Faq7$$\"3!ph&f3oBYLF2$!3)>n>)osS ]NF2$!3O!=Rz*)oy`\"Faq7$$\"3p3F!Hk;Ei$F2$!3Ky)y'fqw*f\"Faq7$$\"3'o-z\" =(zao$F2$!3Q]6Y\\y1`;Faq7$$\"3+uwmhNP`PF2$!3(>`JY/6+r\"Faq7$$\"3>7)3aa 9N#QF2$!3E[O-HU9omcAWA.%F2$!3S&4_2z@o$>Faq7$$\"3eHDx%*G[) 4%F2$!3Ae#[2\\f*))>Faq7$$\"3SqVS7o?pTF2$!3eCKru%pQ/#Faq7$$\"3P/)>M>$HL UF2$!3QV.kw:%H4#Faq7$$\"3%p7,``cLI%F2$!35j(fePPe9#Faq7$$\"3)*Qv%)z1GpV F2$!3AU,?LJ)[>#Faq7$$\"3Ekt21/>QWF2$!3E%eE))=#RXAFaq7$$\"3;B#=!fAc0XF2 $!3e#)eH$o>SH#Faq7$$\"3AQ*[`M%4wXF2$!3;8Ss*3CTM#Faq7$$\"3+CFUF^-WYF2$! 35o#)\\G\"*f\"R#Faq7$$\"3V?MbjT\\8ZF2$!3Oc`taINRCFaq7$$\"3A'z!*4'zQ#y% F2$!3_?^N#=9f[#Faq7$$\"3-LF!e?%pX[F2$!3&y2oZo(*z_#Faq7$$\"3xuKY1.D=\\F 2$!3u^G&zK.ad#Faq7$$\"3+>;%yMXJ)\\F2$!38*4$R\"Rbqh#Faq7$$\"3MYCD(*pL_] F2$!39;-q.yogEFaq7$$\"3gQTRMAc=^F2$!3T!Gc_\\*p,FFaq7$$\"3Y+++'HI(*=&F2 $!3#GA\"4-l&\\u#Faq-I'COLOURGF*6&I$RGBGF*$\"#5!\"\"$\"\"!Fj[lFi[l-I+AX ESLABELSGF*6$Q\"tF$Q!F$-I%VIEWGF*6$;$\"+'42V\">!\"*$\"+'HI(*=&Ff\\lI(D EFAULTGF*" }}{PARA 13 "" 1 "" {TEXT 202 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%+AXESLABELSG6'Q\"t6\"Q!F'-%%FONTG6$%*HELVETICAG\"#5%+ HORIZONTALGF.-%'CURVESG6$7S7$$\"\"!F5$\"3y!#;7$$\"3?'f&Q* oWE<%!#>$\"3ycE^\\M(3&>F87$$\"3r)35E_SK!yF<$\"3)Q4JCCb%3>F87$$\"3'3dB \\_A')=\"!#=$\"3Oim:@K5h=F87$$\"3!o:**[YF'*f\"FG$\"31#HXIg,Q\"=F87$$\" 3$y0C'*)RhnFG$\"3'Q/L)HdBY7F87$$\"37h/!\\aCl=(FG$\"3aFx)R?F8? 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HighTime); 1; XDown := plot(rhs(DownPOSITION), t = HighTime .. HitsGr ound); 1; plots[display](XUp, XDown); 1;" "C(>I$XUpG6\"-I%plotG6$%*pro tectedGI(_syslibGF%6$-I$rhsGF)6#I+UpPOSITIONGF%/I\"tGF%;\"\"!I)HighTim eGF%\"\"\">I&XDownGF%-F'6$-F-6#I-DownPOSITIONGF%/F1;F4I+HitsGroundGF%F 5-&I&plotsGF(6#I(displayGF%6$F$F7F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I$XUpG6\"-I/INTERFACE_PLOTGF$6%-I'CURVESG6$%*protectedGI(_syslibGF$6$7 S7$$\"\"!F1$\"3qK.[$*******H!#;7$$\"3?'f&Q*oWE<%!#>$\"3/C\"y@`EC3$F47$ $\"3r)35E_SK!yF8$\"3GV\"z2%R[_JF47$$\"3'3dB\\_A')=\"!#=$\"3*GC48%zVHKF 47$$\"3!o:**[YF'*f\"FC$\"3&zdq>\"p&\\I$F47$$\"3yLF47$$\"3#HQMx2AzQ#FC$\"3^4Yk;CRWMF47$$\"3ep4.\\jg!y#FC$\"3YLpPdPA6 NF47$$\"3Oal9%)4s'=$FC$\"3G(4l-W>&yNF47$$\"3m;oZ/K`\"f$FC$\"3AXZ7$[oPk $F47$$\"3nGL$3LKz+%FC$\"3Cz/\"ek!**3PF47$$\"3'Q\"*yz!ppuVFC$\"33V$H\"3 p&[w$F47$$\"3_15*Q&pe(y%FC$\"3hC$Q6_()f#QF47$$\"33t7+mB<-_FC$\"3y.0zUH ]&)QF47$$\"3$QFy8B-g(3L'4! *RF47$$\"3YlkTj9$fR'FC$\"3'oizT3Fl/%F47$$\"3Ydx!>'*)RhnFC$\"3_0gRq8y#4 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1;" "C$I+HitsGroun dG6\"\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+'HI(*=&!\"*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 50 "The ball's highest position is ab out 48.54 meters." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "HighestP osition; 1;" "C$I0HighestPositionG6\"\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+McUa[!\")" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }