{VERSION 4 0 "IBM INTEL NT" "4.0" }
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1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
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{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
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11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "
Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }
}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 379 "# set-up position f
unctions xt, yt(rising), yft(falling), \n# Constant of integation: cr,
 maximum height: hh, \n# time when maximum height is reached: tt\nxt:=
m/k*ln(1+k*v0*cos(theta)/m*t);\ncr:=arctan(sqrt(k/g/m)*v0*sin(theta));
\nyt:= m/k*ln( cos(cr-sqrt(g*k/m)*t)/cos(cr));\nhh:=m/k*ln(sqrt(1+v0^2
*sin(theta)^2/140^2));\ntt:=sqrt(m/g/k)*cr;\nyft:= hh - m/k*ln(cosh(cr
-sqrt(g*k/m)*t)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xtG*&*&%\"mG
\"\"\"-%#lnG6#,&F(F(*&**%\"kGF(%#v0GF(-%$cosG6#%&thetaGF(%\"tGF(F(F'!
\"\"F(F(F(F/F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#crG-%'arctanG6#*(
-%%sqrtG6#*&%\"kG\"\"\"*&%\"gGF.%\"mGF.!\"\"F.%#v0GF.-%$sinG6#%&thetaG
F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ytG*&*&%\"mG\"\"\"-%#lnG6#*&-
%$cosG6#,&-%'arctanG6#*(-%%sqrtG6#*&%\"kGF(*&%\"gGF(F'F(!\"\"F(%#v0GF(
-%$sinG6#%&thetaGF(F<*&-F66#*&*&F;F(F9F(F(F'F<F(%\"tGF(F(F(-F66#,&F(F(
*&*(F9F()F=\"\"#F()F>FNF(F(*&F;F(F'F(F<F(F(F(F(F9F<" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#hhG*&*&%\"mG\"\"\"-%#lnG6#,$*$-%%sqrtG6#,&\"&+'>F(
*&)%#v0G\"\"#F()-%$sinG6#%&thetaGF6F(F(F(#F(\"$S\"F(F(%\"kG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ttG*&-%%sqrtG6#*&%\"mG\"\"\"*&%\"gG
F+%\"kGF+!\"\"F+-%'arctanG6#*(-F'6#*&F.F+*&F-F+F*F+F/F+%#v0GF+-%$sinG6
#%&thetaGF+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yftG,&*&*&%\"mG\"
\"\"-%#lnG6#,$*$-%%sqrtG6#,&\"&+'>F)*&)%#v0G\"\"#F))-%$sinG6#%&thetaGF
7F)F)F)#F)\"$S\"F)F)%\"kG!\"\"F)*&*&F(F)-F+6#-%%coshG6#,&-%'arctanG6#*
(-F06#*&F?F)*&%\"gGF)F(F)F@F)F6F)F9F)F@*&-F06#*&*&FQF)F?F)F)F(F@F)%\"t
GF)F)F)F)F?F@F@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "# plug \+
in values for m,k,g, v0(initial velocity), theta( angle of elevation)
\nrule:= \{m=.01, k=.32/140^2, g=32, v0=175, theta=41*Pi/180\};" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ruleG<'/%\"mG$\"\"\"!\"#/%\"kG$\"+h
IlK;!#9/%\"gG\"#K/%#v0G\"$v\"/%&thetaG,$%#PiG#\"#T\"$!=" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "# Plug these values into the funct
ions\nx1:=subs( rule, xt); y1:=subs( rule, yt);\nh1:=subs(rule,hh);  t
1:=subs(rule,tt); y2:= subs(rule,yft);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#x1G,$-%#lnG6#,&\"\"\"F**($\"+dG9dG!#5F*-%$cosG6#,$%#PiG#\"#T
\"$!=F*%\"tGF*F*$\"+,++Dh!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1
G,$-%#lnG6#*&-%$cosG6#,&-%'arctanG6#,$-%$sinG6#,$%#PiG#\"#T\"$!=$\"+++
+]7!\"*!\"\"*&$\"+'G9dG#!#5\"\"\"%\"tGFBFBFB-%%sqrtG6#,&FBFB*&$\"+++]i
:F<FB)F2\"\"#FBFBFB$\"+,++Dh!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#h1G,$-%#lnG6#,$*$-%%sqrtG6#,&\"&+'>\"\"\"*&\"&D1$F0)-%$sinG6#,$%#PiG#
\"#T\"$!=\"\"#F0F0F0#F0\"$S\"$\"+,++Dh!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#t1G,$-%'arctanG6#,$-%$sinG6#,$%#PiG#\"#T\"$!=$\"++++
]7!\"*$\"++++vVF4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&-%#lnG6#,
$*$-%%sqrtG6#,&\"&+'>\"\"\"*&\"&D1$F0)-%$sinG6#,$%#PiG#\"#T\"$!=\"\"#F
0F0F0#F0\"$S\"$\"+,++Dh!\"(*&$\"+,++DhFAF0-F'6#-%%coshG6#,&-%'arctanG6
#,$F4$\"++++]7!\"*!\"\"*&$\"+'G9dG#!#5F0%\"tGF0F0F0FR" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "# Plot the trajectory\nplot( [ [x1,
y1,t=0..t1],[x1,y2,t=t1..6]],color=red);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6#7S7$$\"\"!F)F(7$$\"35
$[T.)=X!f)!#<$\"3Uf$\\F1%H1uF-7$$\"3w4EiDu\"of\"!#;$\"3m2a'3A\"zm8F37$
$\"3!ePXjSRgT#F3$\"3%*[(od\"*G60#F37$$\"3v%e)3L>xHKF3$\"3:\"o5k7N#>FF3
7$$\"3EL')\\RK/HSF3$\"3!o9cuwARO$F37$$\"3uFHcQm'3w%F3$\"3&3Y9^KdR%RF37
$$\"37&enmKC&4bF3$\"3moU<>(yp_%F37$$\"3o,$HoE!GuiF3$\"3:*o&Q!R!\\6^F37
$$\"3(4>\\:t(>FqF3$\"37&y\"Hmi!en&F37$$\"3Ed+0:)G@z(F3$\"3**y!=6\">aPi
F37$$\"3cCc%4hd!e%)F3$\"3NbvY=h&or'F37$$\"3g!H$*GCt\"*>*F3$\"3UR/uxKTR
sF37$$\"3L['HnK<W$**F3$\"3]K.i2dDYxF37$$\"3sYV!=pqM1\"!#:$\"3tqfPgF.=#
)F37$$\"3y+:S)Qxj7\"Fjo$\"3#\\w3L8)\\K')F37$$\"3jL*=yC[.?\"Fjo$\"3X()z
z7hI3\"*F37$$\"3!\\ft?$)>BE\"Fjo$\"3U\"3nB\">5(\\*F37$$\"3GM=&3OFOL\"F
jo$\"3*=Y](z,7L**F37$$\"3%\\Cl:KhgR\"Fjo$\"3A%y:oKo/.\"Fjo7$$\"3i%=T]'
p$QY\"Fjo$\"3%o'\\x40qp5Fjo7$$\"3F\"z'Q)p&oF:Fjo$\"3(o;U'y[e06Fjo7$$\"
3=1Y4[Jg$f\"Fjo$\"3J/FAJ?^T6Fjo7$$\"3#z7kcQ<Nl\"Fjo$\"3y9&p=QdJ<\"Fjo7
$$\"3S\"zCnl#\\<<Fjo$\"3^/Y%\\7he?\"Fjo7$$\"3iL1D\\\\C$y\"Fjo$\"3X&y>X
:w#Q7Fjo7$$\"3%fg;kU8*R=Fjo$\"3krD@xj@l7Fjo7$$\"3*)pc$3qL0!>Fjo$\"3M&=
?&3**)HH\"Fjo7$$\"3)3E(3&fOD'>Fjo$\"36GV!R.`-K\"Fjo7$$\"3(pD%y_HfA?Fjo
$\"3i(R^u$4`X8Fjo7$$\"3];4S!QX,3#Fjo$\"3gPf#QF(oo8Fjo7$$\"3g&RlBH?M9#F
jo$\"3ok>D&y5HR\"Fjo7$$\"3m?qmvLs*>#Fjo$\"3;I7(\\D^LT\"Fjo7$$\"3-1\"[[
0t#fAFjo$\"3pG)*)Go+QV\"Fjo7$$\"3%>`SvTQFJ#Fjo$\"3iHIG[@6^9Fjo7$$\"3C`
BBi5mqBFjo$\"3#flrWA?(o9Fjo7$$\"3h@f)43mYU#Fjo$\"3GV2Cay.%[\"Fjo7$$\"3
cAS/fCh![#Fjo$\"3C\"f_,;g()\\\"Fjo7$$\"3tu3!>j?[`#Fjo$\"3(e7rP3')=^\"F
jo7$$\"3oUzLn@1\"f#Fjo$\"3$Gmu<\\!HC:Fjo7$$\"3YdmMtbuWEFjo$\"33s62w$\\
\\`\"Fjo7$$\"3A0gkzA;*p#Fjo$\"33Nt&><ZXa\"Fjo7$$\"3Yz^\\(4bEv#Fjo$\"3S
[-j*zoFb\"Fjo7$$\"3!ez\\A$4S,GFjo$\"3YQ\"oa:)=f:Fjo7$$\"3aWZ7xhzcGFjo$
\"39-ao\\5@l:Fjo7$$\"3-iYbO9#f!HFjo$\"3Cp-^7FRp:Fjo7$$\"3gQ]!3\")oy&HF
jo$\"3gk3CH%*fs:Fjo7$$\"3PHZq(zzr+$Fjo$\"3I1>3g)fWd\"Fjo7$$\"3)4*Q1^Bt
fIFjo$\"3_3@z))>9v:Fjo-F$6#7S7$Fcz$\"3m2@z))>9v:Fjo7$$\"32$=rLIH=6$Fjo
$\"3K)>4]8gWd\"Fjo7$$\"3[(pW&\\3!o:$Fjo$\"3S=^(QfdFd\"Fjo7$$\"3:p)RMp%
)p?$Fjo$\"3k8G)Q]5'p:Fjo7$$\"3ca723$*3dKFjo$\"3S=%o5>E^c\"Fjo7$$\"3qIk
2=@b1LFjo$\"3O2LN$z`$f:Fjo7$$\"3a]PCbj0_LFjo$\"3)R_n\">s$Gb\"Fjo7$$\"3
%>5*Q'z>))R$Fjo$\"3Ju'f1A6\\a\"Fjo7$$\"3)='=8l*4oW$Fjo$\"3%Q(f^9iXN:Fj
o7$$\"3!f9qv#\\F%\\$Fjo$\"3!yQR-[iZ_\"Fjo7$$\"3vz(>Nr<Fa$Fjo$\"3)fA^,R
XC^\"Fjo7$$\"3?5bT&3r]e$Fjo$\"3-Pp^2U\\+:Fjo7$$\"3\\GTXDJSKOFjo$\"3a&p
jZ))4e[\"Fjo7$$\"39m\"e1Kk&zOFjo$\"3)Qm![%Rg(p9Fjo7$$\"3-WxiT=nCPFjo$
\"3u=\"\\&GH1`9Fjo7$$\"3Ks.3lzMlPFjo$\"3Z(>eK**eoV\"Fjo7$$\"3L&)*Rs$oO
8QFjo$\"3cu*f_u3jT\"Fjo7$$\"3k]fHWEv`QFjo$\"33;mF(p;yR\"Fjo7$$\"3[a'R3
L)R+RFjo$\"3[MxfbU1v8Fjo7$$\"3z_j)eM$RTRFjo$\"3wJm!)px\"QN\"Fjo7$$\"3'
Qy<>%z0')RFjo$\"3c.k_9-KH8Fjo7$$\"3v,=.#e)GGSFjo$\"3kL;Q2t%[I\"Fjo7$$
\"3QkA*3hV?2%Fjo$\"31;/Yl48y7Fjo7$$\"3\"z!*)o<4&>6%Fjo$\"3Q>#fH;VDD\"F
jo7$$\"3G&4PZ$oqaTFjo$\"3cIQJy?#QA\"Fjo7$$\"3%[fFPW/))>%Fjo$\"3=j'yXFo
F>\"Fjo7$$\"3ojz*GvMpB%Fjo$\"3=u!>9#Gtk6Fjo7$$\"3slU%yj^yF%Fjo$\"3Z)>o
cR:M8\"Fjo7$$\"3mkB$=nP)>VFjo$\"3I#)*)Hf.%**4\"Fjo7$$\"3u![$eshjgVFjo$
\"3It=iD35m5Fjo7$$\"3'3'G-?Q&)*R%Fjo$\"3M(=@ltVB.\"Fjo7$$\"3.SlWZh5VWF
jo$\"3&zATKbaq$**F37$$\"3+])f#p9r\"[%Fjo$\"3!RQ&\\p5hz&*F37$$\"3]Di*)[
SmAXFjo$\"3Q-<ifQP(=*F37$$\"3'['3Wr\"Q&fXFjo$\"3WwSsXshA))F37$$\"3g)y<
p#*)f*f%Fjo$\"3*H5&RM#=QT)F37$$\"3x(*pJ7_0PYFjo$\"3e\\W/F-t>!)F37$$\"3
73<2.X'fn%Fjo$\"3#*y5c\\/9)f(F37$$\"38]k:szw8ZFjo$\"3A2<bNoawrF37$$\"3
'>C@[G'4`ZFjo$\"3CQe$**\\X`s'F37$$\"3+\\of#)ot!z%Fjo$\"3s(>,?h79G'F37$
$\"3BN&*pz?**G[Fjo$\"3'>(\\l4d0=eF37$$\"3E*[Bw)fpm[Fjo$\"3Qe$H#4eJ\\`F
37$$\"3$>>_U_Q6!\\Fjo$\"3t4tYdxh5\\F37$$\"38=bNAoPS\\Fjo$\"3Ec=Jp5d)R%
F37$$\"3/Mh)\\Kg_(\\Fjo$\"3cu.nK\"\\B$RF37$$\"3B:UoqeB7]Fjo$\"3I)3+o$[
#oU$F37$$\"3IUD$)Q$=u/&Fjo$\"3#R#e_s%\\\\$HF37$$\"3W?(Hlx-]3&Fjo$\"3iz
_lj#exR#F3-%+AXESLABELSG6$Q!6\"F`jl-%'COLOURG6&%$RGBG$\"*++++\"!\")F(F
(-%%VIEWG6$%(DEFAULTGF\\[m" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "# determine when the ball lands\nland:=fsolve(y2=0,t=
5.7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%landG$\"+\"p'oyi!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "# Determine where the ball l
ands\nevalf(subs( t=land, x1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
+E?SV_!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "# determine t
he maximum height\nevalf( h1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+
*)>9v:!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7
 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }