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

If an object is moving under the influence of gravity and friction, then one may use Newton's second law to write, 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, where 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 is a velocity-dependent force used to model the effects of friction in the system. Most often these forces take the foillowing form: 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. In order to determine the form of the velocity function one must of course specify a particular power, n. In MAple however it is sufficient to define the equation in general. i.e., restart: with(plots): eq:=(n)->m*diff(v(t),t)=-m*g-k[n]*m*v(t)^n: eq(n);

Warning, the name changecoords has been redefined

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtRiQ2JS1JI21pR0YlNjlRIm1GKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOi8lKnN1YnNjcmlwdEdGOi8lLHN1cGVyc2NyaXB0R0Y6LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GKC8lJ29wYXF1ZUdGOi8lK2V4ZWN1dGFibGVHRjovJSlyZWFkb25seUdGPS8lKWNvbXBvc2VkR0Y6LyUqY29udmVydGVkR0Y6LyUraW1zZWxlY3RlZEdGOi8lLHBsYWNlaG9sZGVyR0Y6LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RigvJSptYXRoY29sb3JHRkYvJS9tYXRoYmFja2dyb3VuZEdGSS8lK2ZvbnRmYW1pbHlHRjQvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoLyUpbWF0aHNpemVHRjctSSNtb0dGJTYzUTEmSW52aXNpYmxlVGltZXM7RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y6LyUqc2VwYXJhdG9yR0Y6LyUnbHNwYWNlR1EkMGVtRigvJSdyc3BhY2VHRl1wLyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lMGZvbnRfc3R5bGVfbmFtZUdGWi8lJXNpemVHRjcvJStmb3JlZ3JvdW5kR0ZGLyUrYmFja2dyb3VuZEdGSS1GJDYlLUZhbzYzUSIoRigvRmVvUSdwcmVmaXhGKC9GaG9GPUZpby9GXHBRLnRoaW5tYXRoc3BhY2VGKC9GX3BGYXIvRmFwRj1GYnBGZHBGZ3BGanBGXHFGXnFGYHFGYnFGZHFGZnEtRiQ2JS1JJm1mcmFjR0YlNiotRiQ2Iy1GYW82M1EwJkRpZmZlcmVudGlhbEQ7RihGXXJGZ29GaW9GW3BGXnBGYHBGYnBGZHBGZ3BGanBGXHFGXnFGYHFGYnFGZHFGZnEtRiQ2Iy1GJDYkRltzLUYvNjlRInRGKEYyRjVGOEY7Rj5GQEZCRkRGR0ZKRkxGTkZQRlJGVEZWRlhGZW5GZ25GaW5GW29GXm8vJS5saW5ldGhpY2tuZXNzR1EiMUYoLyUrZGVub21hbGlnbkdRJ2NlbnRlckYoLyUpbnVtYWxpZ25HRmpzLyUpYmV2ZWxsZWRHRjpGZHFGZnFGYG8tRiQ2JS1GLzY5USJ2RihGMkY1RjhGO0Y+RkBGQkZERkdGSkZMRk5GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vLUZhbzYzUTAmQXBwbHlGdW5jdGlvbjtGKEZkb0Znb0Zpb0ZbcEZecEZgcEZicEZkcEZncEZqcEZccUZecUZgcUZicUZkcUZmcS1GJDYlRmpxLUYkNiNGYnMtRmFvNjNRIilGKC9GZW9RKHBvc3RmaXhGKEZfckZpb0Zgci9GX3BRMnZlcnl0aGlubWF0aHNwYWNlRihGY3JGYnBGZHBGZ3BGanBGXHFGXnFGYHFGYnFGZHFGZnFGW3UtRmFvNjNRIj1GKEZkb0Znb0Zpby9GXHBRL3RoaWNrbWF0aHNwYWNlRigvRl9wRmZ1RmBwRmJwRmRwRmdwRmpwRlxxRl5xRmBxRmJxRmRxRmZxLUYkNiYtRmFvNjNRKiZ1bWludXMwO0YoRl1yRmdvRmlvRltwRl5wRmBwRmJwRmRwRmdwRmpwRlxxRl5xRmBxRmJxRmRxRmZxLUYkNiVGLkZgby1GLzY5USJnRihGMkY1RjhGO0Y+RkBGQkZERkdGSkZMRk5GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vLUZhbzYzUSgmbWludXM7RihGZG9GZ29GaW8vRlxwUTBtZWRpdW1tYXRoc3BhY2VGKC9GX3BGZnZGYHBGYnBGZHBGZ3BGanBGXHFGXnFGYHFGYnFGZHFGZnEtRiQ2Jy1JJW1zdWJHRiU2Ji1GLzY5USJrRihGMkY1RjhGO0Y+RkBGQkZERkdGSkZMRk5GUEZSRlRGVkZYRmVuRmduRmluRltvRl5vLUYkNiMtRi82OVEibkYoRjJGNUY4RjtGPkZARkJGREZHRkpGTEZORlBGUkZURlZGWEZlbkZnbkZpbkZbb0Zeby8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYoLyUscGxhY2Vob2xkZXJHRjpGYG9GLkZgby1JJW1zdXBHRiU2JUZfdEZidy8lMXN1cGVyc2NyaXB0c2hpZnRHRmd3NyMtX0YpSSxtcHJpbnRzbGFzaEdGKDYkNyMvKiZJIm1HRigiIiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkidkdGKDYjSSJ0R0YoRmB5Rmh4LCYqJkZneEZoeEkiZ0dGKEZoeCEiIiooJkkia0dGKDYjSSJuR0YoRmh4Rmd4Rmh4KUZdeUZpeUZoeEZkeUZkeA==

Once the equation is defined, a specific value of n may be chosen by passing it to the procedure. i.e., eq(1); eq(2);

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

In order to solve these equations with Maple, one needs to use the dsolve command. The basic syntax for the dsolve command is as follows: dsolve({equations, initial conditions},functions); The initial conditions are specified by giving the value of the functions sought at a specific time. Because the solutions here depend upon the value of n chosen we once again "build" a siolution that depends upon n, and we specify the velocity. Once this is done we simply call the solution procedure with specific values of n to obatain the solution. sol:=(n)->dsolve({eq(n),v(0)=v0},v(t)): sol(1); sol(2);

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

In order to use the algebraic results that Maple gives you, you have to tell Maple that the result, stored on the right hand side (rhs) of the result printed to the screen, will depend upon values that are specified by you. To do this the rhs and unapply commands can be used togetner to define a new function that depends upon the desired variables. For example, v1:=unapply(rhs(sol(1)),g,k[1],v0,t): v1(g,k[1],v0,t);

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

To plot the velocity for particular values, simply pass the function to the plot command as illustrated below: plot(v1(9.8,0.1,500,t),t=0..100, labels=["t","v"],title="Velocity n=1");

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

Now that the velocity has been obtained the position can be found by integrating the resulting velocity function. That is, symbolically one would write, 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. To define this position function in Maple we first define the equation, and then use the unapply command to "build" a function that depends upon the desired variables. (Note also that to perform the integration symbolically a temporary variable has been introduced so that 't' can be used in the result.) pos1:=y0+int(v1(g,k[1],v0,temp),temp=0..t): y1:=unapply(pos1,g,k[1],v0,y0,t): y1(g,k[1],v0,y0,t);

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

To obtain a plot of the position, simply choose values for the parameters. That is, using the same damping coefficient and initial velocity as above, one obtains a plot of the position of the object. plot(y1(9.8,0.1,500,200,t),t=0..100, labels=["t","x"],title="Position (n=1)");

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2OVEhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGOi8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUqbWF0aGNvbG9yR0ZDLyUvbWF0aGJhY2tncm91bmRHRkYvJStmb250ZmFtaWx5R0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKW1hdGhzaXplR0Y0 It is easiest to define each of the functions as being dependent on the position , the initial velocity, and the angle of launch, . This can be done as follows: g:=9.8: y1:=(x,v0,theta)->tan(theta*Pi/180)*x-g/(2*v0^2*cos(theta*Pi/180)^2)*x^2; y2:=(x,v0,theta,k)->tan(theta*Pi/180)*x+g/k^2*(k*x/(v0*cos(theta*Pi/180))+ln(1-k*x/(v0*cos(theta*Pi/180))));

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

Then you can plot each function with the appropriate values for the initiial velocity, angle, and/or the drag coefficient. e.g., for the case of no friction, and using values of and , the motion would look like this: (Note that the vertical range has been specified with the y=ymin..ymax option) plot(y1(x,600,30),x=0..50000,y=0..5000);

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

To find the point at which the projectile hits the ground - its' range, you can use the solve function as follows: solve(y1(x,600,30)=0,x);

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

Hence the total range of the projectile is, 31,813.2 m. Using the same commands we can plot the same trajectory with air resistance for a drag coefficient of k=0.02 in the following manner: (again, and ) plot(y2(x,600,30,0.02),x=0..50000,y=0..5000);

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

solve(y2(x,600,30,0.02)=0,x);

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

With friction, the total range of the projectile is only, 16,848.4 m ! To plot several different trajectories at the same time, you need to enclose the list of functions in square brackets, [ ]. It is often helpful to define the plot first like this, trajectories:= plot([y1(x,600,30), y2(x,600,30,0.01), y2(x,600,30,0.02), y2(x,600,30,0.04)], x=0..50000,y=0..5000, color=black,linestyle=[1,2,3,4], title="Effects of Air Resistance on Projectile Range", labels=["Range (m)","Height (m)"]): Many useful options have been added here to include a title and labels, etc. Perhaps the most important one used however is the linestyle option, which indicates that the plots should be shown with solid, dotted, dashed, and dash-dotted lines, for the values of 1, 2, 3, and 4 respectively. Once the plot has been defined you can then load the plots package and display the plot as follows: with(plots): display(trajectories);

6)-I'CURVESG6$%*protectedGI(_syslibG6"6%7S7$$""!F-F,7$$"3YLLL3x&)*3"!#9$"3c%=,ebMn2'!#:7$$"3(pm;H2P"Q?F1$"3(Qfq2`J85"F17$$"3mLL$eRwX5$F1$"3*\NpZ+4vh"F17$$"3-ML$3x%3yTF1$"3g)=kD<<a4#F17$$"3Anm"z%4\Y_F1$"3Fx#*ftI_HDF17$$"3YLLeR-/PiF1$"3'emJ<s")\*GF17$$"3;++DcmpisF1$"34#GS_!Q'eB$F17$$"3:MLe*)>VB$)F1$"3q@+]02C[NF17$$"3+,+DJbw!Q*F1$"3,U_uNH(*=QF17$$"3umm;/j$o/"!#8$"3IdyX=z6bSF17$$"3XLL3_>jU6Fjn$"3'[9[KJ_vA%F17$$"3E++]i^Z]7Fjn$"3OFlzGt"=Q%F17$$"31++](=h(e8Fjn$"3?'R!H_AC%\%F17$$"3E++]P[6j9Fjn$"3a*p@SD9Bc%F17$$"3SL$e*[z(yb"Fjn$"3Ct]W]l))*e%F17$$"3wmm;a/cq;Fjn$"3yK4&*)[]-e%F17$$"3ummm;t,m<Fjn$"3kLaWR,.OXF17$$"3%***\iSj0x=Fjn$"37?y2(GzHW%F17$$"3ymmm"pW`(>Fjn$"3iqFy7ZFBVF17$$"3Q+]i!f#=$3#Fjn$"3gPy`;(*f^TF17$$"3;+](=xpe=#Fjn$"3m=OvV9*)[RF17$$"33nm"H28IH#Fjn$"3YS%)*f3'e'p$F17$$"3#pm"zpSS"R#Fjn$"3@dOT10>GMF17$$"3[LL3_?`(\#Fjn$"3cV`k?()H*4$F17$$"3WL$e*)>pxg#Fjn$"3u[8EzlQ9FF17$$"3-+]Pf4t.FFjn$"3&\&)elI4MM#F17$$"3iLLe*Gst!GFjn$"33%\(4z.?0>F17$$"3&******\#RW9HFjn$"3yl"e#[Ha69F17$$"3)****\7j#>>IFjn$"3/[Gv(>&G$)))F47$$"3>+]i!RU07$Fjn$"3[k><4v$=W$F47$$"3K++v=S2LKFjn$!3T`2Ft'fn.$F47$$"3Fmmm"p)=MLFjn$!3e))p^lx6]#*F47$$"3=++](=]@W$Fjn$!3Bx3k$p%QH;F17$$"39L$e*[$z*RNFjn$!3Q7+-$p(=/BF17$$"3%3++DYKpk$Fjn$!3wo`>pQn"3$F17$$"3'pm"H2qcZPFjn$!37x.!*R,9^QF17$$"3c+]7."fF&QFjn$!31+$=#psu%p%F17$$"3kmm;/OgbRFjn$!3+.vmghNebF17$$"3++]ilAFjSFjn$!3nl))QH'3O]'F17$$"3'RLLL)*pp;%Fjn$!3Kep%pfwPX(F17$$"3#RL$3xe,tUFjn$!3EKC10l#eY)F17$$"3in;HdO=yVFjn$!3E?^S!Q3)4&*F17$$"3#4++]#>#[Z%Fjn$!3=Kjx:7X]5Fjn7$$"3=nmT&G!e&e%Fjn$!3M\Xv)GC'o6Fjn7$$"3OLLL$)Qk%o%Fjn$!3QV^*o">4y7Fjn7$$"3;+]iSjE!z%Fjn$!3G$*e9p2t)R"Fjn7$$"3S+]P40O"*[Fjn$!3B!zxe6!*z^"Fjn7$$"&++&F-$!3Ur=b"p&G];Fjn-I*LINESTYLEGF(6#"""-I'COLOURGF%6&I$RGBGF%F-F-F--F$6%7YF+7$F/$"31d)pH:sO2'F47$F6$"3wV=]E.I*4"F17$F;$"3.'\)efP@5;F17$F@$"3%)=_+g.Mx?F17$FE$"3]jThKo7$\#F17$FJ$"3:\Lm\,'G$GF17$FO$"37q"Gk#>8OJF17$FT$"3G%e$)z&pX&R$F17$FY$"3!Gl1Ef5jf$F17$Fhn$"3">f'*\I=)RPF17$F^o$"3hlZ'e=\0"QF17$Fco$"3*\%**RuJ`CQF17$Fho$"3e=m.3-)[w$F17$F]p$"3j<lr<$yNj$F17$Fbp$"3EW,<6q3[MF17$Fgp$"3j&p$4#pp19$F17$F\q$"3)G>58rV@!GF17$Faq$"3$ez5\PLDJ#F17$Ffq$"3Y?R$3_?yy"F17$F[r$"3<&G#f+)po5"F17$F`r$"3km:7V:!>\$F47$Fer$!3`1$)[$\+8j&F47$Fjr$!3%HN1")>L$=:F17$F_s$!3#*Rx%4n'=%o#F17$Fds$!3AC!=Mubf0%F17$Fis$!3swkqHlQ%R&F17$F^t$!3uTr'*42d.qF17$Fct$!3k/$>.vD,'))F17$Fht$!3AVW7a:`)3"Fjn7$F]u$!3_Y'owvxgI"Fjn7$Fbu$!3y(Qj@$f8v:Fjn7$Fgu$!3h!GLj4*HW=Fjn7$F\v$!3?WP<a*>P;#Fjn7$Fav$!35V)*>C$f^[#Fjn7$Ffv$!3sAE"eoBf(GFjn7$F[w$!3Y]6@H@B'G$Fjn7$F`w$!3=$>(G!*e"fw$Fjn7$Few$!3C`$onS#4$H%Fjn7$Fjw$!3/W?!3B9w"\Fjn7$F_x$!3\ME*fBaHg&Fjn7$Fdx$!3a#ofZ!\S2kFjn7$Fix$!3)R&G%Q;yOL(Fjn7$F^y$!3OO"R%y^uF$)Fjn7$Fcy$!3M9L0nod)o*Fjn7$$"3F+]P%37^j%Fjn$!3\#y2Kyn&R5!#77$Fhy$!34%[7*oi%z6"F_dl7$$"3Sm"z>6but%Fjn$!3%=ZOBAJ<@"F_dl7$F]z$!3k(*fw`Nf=8F_dl7$$"3G+++DM"3%[Fjn$!3tTB%HD#[O9F_dl7$Fbz$!3O`3e&y/Wd"F_dl7$$"3w\7.#Q?&=\Fjn$!3eN'H]K!=f;F_dl7$$"3%)*\(oa-oX\Fjn$!3U-:GC(zLv"F_dl7$$"3#*\PMF,%G(\Fjn$!39%poRKq"f=F_dl7$Fgz$!3W9/xxacz>F_dl-F\[l6#""#F_[l-F$6%7YF+7$$"37+++4x&)*3"F1$"3!e!)e4&*402'F47$$"3*******R2P"Q?F1$"3+dd_A89(4"F17$$"3#)*****pRwX5$F1$"3FYS#Q(G>-;F17$$"3;+++sZ3yTF1$"3qev0'eZn0#F17$$"3M+++]4\Y_F1$"3ETr53m5]CF17$$"3/+++U-/PiF1$"3/vv!p^gnv#F17$$"3G******empisF1$"3,?&))oTN"4IF17$$"3")*****>*>VB$)F1$"3wRA+?ka#>$F17$$"37+++Mbw!Q*F1$"3OOS=e4B(G$F17$$"3++++0j$o/"Fjn$"33A="RLw0G$F17$$"3"******>&>jU6Fjn$"3s#R[$3&)HvJF17$$"31+++j^Z]7Fjn$"3c([095i(GHF17$$"3/+++)=h(e8Fjn$"3dPJ0c))zADF17$$"31+++Q[6j9Fjn$"35t"zdU?V&>F17$$"33+++\z(yb"Fjn$"3wfa:#Go*e7F17$$"3++++b/cq;Fjn$"3^U6Rn*30j"F47$$"3#)*****pJ<gw"Fjn$!3#*R^%4"f_Y5F17$$"3))*****4Mcq(=Fjn$!3Q"HkmrKw'GF17$$"3')*****>pW`(>Fjn$!3=shC8]!Q'\F17$$"3'******4f#=$3#Fjn$!3!HU@-!o3$)zF17$$"3(******>=EX8#Fjn$!3yL`]q&3hx*F17$$"3)******Hxpe=#Fjn$!3Ae(*f2f:(="Fjn7$$"3$)*****RUT%RAFjn$!3yWlAiizY9Fjn7$$"3/+++uI,$H#Fjn$!3)*o:z8Nsh<Fjn7$$"3;+++B3h<BFjn$!3:&[f"fQHI>Fjn7$$"3"******>d3AM#Fjn$!3sF'Gw9#y<@Fjn7$$"3++++Aj!oO#Fjn$!3y\Fj8$=!GBFjn7$$"35+++rSS"R#Fjn$!3)*oX:lw7mDFjn7$$"3&)*****f1OzT#Fjn$!3Ezx&4-;C'GFjn7$$"3#******>1oWW#Fjn$!3;By["3PC@$Fjn7$$"3'*******fStdCFjn$!3qd9y4db8MFjn7$$"3++++e++rCFjn$!3%Qj26$RmOOFjn7$$"3-+++cgE%[#Fjn$!31n)>M6>m)QFjn7$$"33+++`?`(\#Fjn$!3y%es#)=!4qTFjn7$$"3%******fp68^#Fjn$!3zY>&f[o-^%Fjn7$$"38+++S84DDFjn$!3QhWtB^.8\Fjn7$$"3/+++i6)>`#Fjn$!3mX&4;0)\X^Fjn7$$"3)******H)4()QDFjn$!3y%[iX&)GZS&Fjn7$$"3#******R!3wXDFjn$!3)o$)HkDltp&Fjn7$$"3%)*****fi]Eb#Fjn$!3)**[L21oG.'Fjn7$$"3)******p`&4cDFjn$!3Fp%o$pD&3A'Fjn7$$"35+++[/afDFjn$!3]p-Lp0RDkFjn7$$"3))******e`)Hc#Fjn$!3o"\dmQ'e\mFjn7$$"3-+++q-VmDFjn$!3isog-)3v*oFjn7$$"3;+++"=v)pDFjn$!3]fTm;sjurFjn7$$"3%******>4?Ld#Fjn$!3%R%y(o&**f)[(Fjn7$$"35+++-]wwDFjn$!3+![ZPEp/&yFjn7$$"3))*****H"*4-e#Fjn$!3#HUxA\3sF)Fjn7$$"3-+++C[l$e#Fjn$!3#G@d*p.x'z)Fjn7$$"3=+++M(*4(e#Fjn$!35?"G4Uz-Y*Fjn7$$"3%******\kW0f#Fjn$!3iYh;9QyP5F_dl7$$"33+++c&*)Rf#Fjn$!3+.)fw@Zq="F_dl7$$"3')*****pYMuf#Fjn$!3,IzGd**3S;F_dl7$I*undefinedGF&Fegm-F\[l6#""$F_[l-F$6%7OF+7$$"3W*****\a)G\aF4$"3%["eT"f,24$F47$F\gl$"3CPJ"pXkQ1'F47$$"3++++#R(*Rc"F1$"3]4*Q#>1jY&)F47$Fagl$"3Ge(=RE%Q#4"F17$Ffgl$"3y^(oHr\Me"F17$F[hl$"3!\Mu.QA`+#F17$F`hl$"3YeFYaXIMBF17$Fehl$"30ZgLQd$\`#F17$Fjhl$"3VsJ0h=v,EF17$$"3Q*****\KkIz(F1$"3O:0gi.(Gc#F17$F_il$"3[4CJ->()fCF17$$"3k+++l()4_))F1$"3Ul-h$**))zF#F17$Fdil$"3C(z)4v0K&*>F17$$"3E+++!HkX#**F1$"3SNrXN6bl:F17$Fiil$"3uJ^FBV")*R*F47$$"3/+++;_yq5Fjn$"3VHYOh2Y+eF47$$"31+++GTt%4"Fjn$"3!z&=Pq03B:F47$$"32+++SIo=6Fjn$!3dWDD^5x,OF47$F^jl$!3!*=QH-2D;)*F47$$"31+++aB6c6Fjn$!3Q)p8=@(G#R"F17$$"3/+++bFfp6Fjn$!3SzYz_)zw&=F17$$"3-+++cJ2$="Fjn$!3m(QqWUh)*Q#F17$$"3)******zb`l>"Fjn$!3Tf8[WXP0IF17$$"3'*******eR.57Fjn$!3%pdP)>!)yFPF17$$"3%*******fV^B7Fjn$!3YYEoaHM#f%F17$$"3#******4ca-B"Fjn$!31!)f"y%*GU4&F17$$"33+++iZ*pB"Fjn$!3wU)pTS8_l&F17$$"34+++i\tV7Fjn$!3KICB6\"*)G'F17$Fcjl$!3HA#foH!G9qF17$$"3)******>5fQD"Fjn$!3!p/=W*f=@uF17$$"3%*******RICd7Fjn$!3=&3]!e-biyF17$$"31+++ypig7Fjn$!3#\!Gf<")>W$)F17$$"3++++;4,k7Fjn$!3)GD8(e*oN())F17$$"3%******R&[Rn7Fjn$!3mxd/tXPg%*F17$$"3/+++$zy2F"Fjn$!3yJd%o3j<,"Fjn7$$"3'******>tiTF"Fjn$!3'3112*\L'3"Fjn7$$"33+++qmax7Fjn$!3m:9$p!yMs6Fjn7$$"3/+++31$4G"Fjn$!3YDEN7stt7Fjn7$$"3)******fa9VG"Fjn$!3#>=LwA+pR"Fjn7$$"3#******R[)p(G"Fjn$!3Wb)**z(GI`:Fjn7$$"3-+++BC3"H"Fjn$!3[fF"epLow"Fjn7$$"3%******>OmWH"Fjn$!30?$>:R/E5#Fjn7$$"31++++.&yH"Fjn$!3hRE!>auX#HFjnFdgm-F\[l6#""%F_[l-I+AXESLABELSGF%6$Q*Range~(m)F(Q+Height~(m)F(-I&TITLEGF%6#QNEffects~of~Air~Resistance~on~Projectile~RangeF(-I%VIEWGF%6$;F,Fgz;F,$"%+]F-

In many cases it will be nice to be able to include a legend for your graph, indicating the values of different parameters. The following code may be adapted for use in most situations and includes both lines and text. Note that CURVES is an intrinsic MAPLE plotting structure and is used to draw curves by connecting the popints indicated. Here I have used only two points and so a line results. The TEXT structure is again an intrinsic structure, and the use is straight forward. Here I have chosen to align the text, enclosed in single quotes, to the right of the right of the lines using ALIGNRIGHT. legend:=PLOT( CURVES([[32500,4500],[37500,4500]],LINESTYLE(1)), TEXT([40000,4500],'`k=0.00`',ALIGNRIGHT), CURVES([[32500,4000],[37500,4000]],LINESTYLE(2)), TEXT([40000,4000],'`k=0.01`',ALIGNRIGHT), CURVES([[32500,3500],[37500,3500]],LINESTYLE(3)), TEXT([40000,3500],'`k=0.02`',ALIGNRIGHT), CURVES([[32500,3000],[37500,3000]],LINESTYLE(4)), TEXT([40000,3000],'`k=0.04`',ALIGNRIGHT) ): By itself the legend looks like this: display(legend);

NiotSSdDVVJWRVNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckNyQiJitEJCIlK1g3JCImK3YkRi0tSSpMSU5FU1RZTEVHRig2IyIiIi1JJVRFWFRHRiU2JTckIiYrKyVGLUknaz0wLjAwR0YoSStBTElHTlJJR0hUR0YlLUYkNiQ3JDckRiwiJStTNyRGL0Y/LUYxNiMiIiMtRjU2JTckRjhGP0knaz0wLjAxR0YoRjotRiQ2JDckNyRGLCIlK043JEYvRkwtRjE2IyIiJC1GNTYlNyRGOEZMSSdrPTAuMDJHRihGOi1GJDYkNyQ3JEYsIiUrSTckRi9GWS1GMTYjIiIlLUY1NiU3JEY4RllJJ2s9MC4wNEdGKEY6

But when you put it together with the trajectories plot, you get a high-quality, content-rich plot: display(trajectories,legend);

61-I'CURVESG6$%*protectedGI(_syslibG6"6%7S7$$""!F-F,7$$"3YLLL3x&)*3"!#9$"3c%=,ebMn2'!#:7$$"3(pm;H2P"Q?F1$"3(Qfq2`J85"F17$$"3mLL$eRwX5$F1$"3*\NpZ+4vh"F17$$"3-ML$3x%3yTF1$"3g)=kD<<a4#F17$$"3Anm"z%4\Y_F1$"3Fx#*ftI_HDF17$$"3YLLeR-/PiF1$"3'emJ<s")\*GF17$$"3;++DcmpisF1$"34#GS_!Q'eB$F17$$"3:MLe*)>VB$)F1$"3q@+]02C[NF17$$"3+,+DJbw!Q*F1$"3,U_uNH(*=QF17$$"3umm;/j$o/"!#8$"3IdyX=z6bSF17$$"3XLL3_>jU6Fjn$"3'[9[KJ_vA%F17$$"3E++]i^Z]7Fjn$"3OFlzGt"=Q%F17$$"31++](=h(e8Fjn$"3?'R!H_AC%\%F17$$"3E++]P[6j9Fjn$"3a*p@SD9Bc%F17$$"3SL$e*[z(yb"Fjn$"3Ct]W]l))*e%F17$$"3wmm;a/cq;Fjn$"3yK4&*)[]-e%F17$$"3ummm;t,m<Fjn$"3kLaWR,.OXF17$$"3%***\iSj0x=Fjn$"37?y2(GzHW%F17$$"3ymmm"pW`(>Fjn$"3iqFy7ZFBVF17$$"3Q+]i!f#=$3#Fjn$"3gPy`;(*f^TF17$$"3;+](=xpe=#Fjn$"3m=OvV9*)[RF17$$"33nm"H28IH#Fjn$"3YS%)*f3'e'p$F17$$"3#pm"zpSS"R#Fjn$"3@dOT10>GMF17$$"3[LL3_?`(\#Fjn$"3cV`k?()H*4$F17$$"3WL$e*)>pxg#Fjn$"3u[8EzlQ9FF17$$"3-+]Pf4t.FFjn$"3&\&)elI4MM#F17$$"3iLLe*Gst!GFjn$"33%\(4z.?0>F17$$"3&******\#RW9HFjn$"3yl"e#[Ha69F17$$"3)****\7j#>>IFjn$"3/[Gv(>&G$)))F47$$"3>+]i!RU07$Fjn$"3[k><4v$=W$F47$$"3K++v=S2LKFjn$!3T`2Ft'fn.$F47$$"3Fmmm"p)=MLFjn$!3e))p^lx6]#*F47$$"3=++](=]@W$Fjn$!3Bx3k$p%QH;F17$$"39L$e*[$z*RNFjn$!3Q7+-$p(=/BF17$$"3%3++DYKpk$Fjn$!3wo`>pQn"3$F17$$"3'pm"H2qcZPFjn$!37x.!*R,9^QF17$$"3c+]7."fF&QFjn$!31+$=#psu%p%F17$$"3kmm;/OgbRFjn$!3+.vmghNebF17$$"3++]ilAFjSFjn$!3nl))QH'3O]'F17$$"3'RLLL)*pp;%Fjn$!3Kep%pfwPX(F17$$"3#RL$3xe,tUFjn$!3EKC10l#eY)F17$$"3in;HdO=yVFjn$!3E?^S!Q3)4&*F17$$"3#4++]#>#[Z%Fjn$!3=Kjx:7X]5Fjn7$$"3=nmT&G!e&e%Fjn$!3M\Xv)GC'o6Fjn7$$"3OLLL$)Qk%o%Fjn$!3QV^*o">4y7Fjn7$$"3;+]iSjE!z%Fjn$!3G$*e9p2t)R"Fjn7$$"3S+]P40O"*[Fjn$!3B!zxe6!*z^"Fjn7$$"&++&F-$!3Ur=b"p&G];Fjn-I*LINESTYLEGF(6#"""-I'COLOURGF%6&I$RGBGF%F-F-F--F$6%7YF+7$F/$"31d)pH:sO2'F47$F6$"3wV=]E.I*4"F17$F;$"3.'\)efP@5;F17$F@$"3%)=_+g.Mx?F17$FE$"3]jThKo7$\#F17$FJ$"3:\Lm\,'G$GF17$FO$"37q"Gk#>8OJF17$FT$"3G%e$)z&pX&R$F17$FY$"3!Gl1Ef5jf$F17$Fhn$"3">f'*\I=)RPF17$F^o$"3hlZ'e=\0"QF17$Fco$"3*\%**RuJ`CQF17$Fho$"3e=m.3-)[w$F17$F]p$"3j<lr<$yNj$F17$Fbp$"3EW,<6q3[MF17$Fgp$"3j&p$4#pp19$F17$F\q$"3)G>58rV@!GF17$Faq$"3$ez5\PLDJ#F17$Ffq$"3Y?R$3_?yy"F17$F[r$"3<&G#f+)po5"F17$F`r$"3km:7V:!>\$F47$Fer$!3`1$)[$\+8j&F47$Fjr$!3%HN1")>L$=:F17$F_s$!3#*Rx%4n'=%o#F17$Fds$!3AC!=Mubf0%F17$Fis$!3swkqHlQ%R&F17$F^t$!3uTr'*42d.qF17$Fct$!3k/$>.vD,'))F17$Fht$!3AVW7a:`)3"Fjn7$F]u$!3_Y'owvxgI"Fjn7$Fbu$!3y(Qj@$f8v:Fjn7$Fgu$!3h!GLj4*HW=Fjn7$F\v$!3?WP<a*>P;#Fjn7$Fav$!35V)*>C$f^[#Fjn7$Ffv$!3sAE"eoBf(GFjn7$F[w$!3Y]6@H@B'G$Fjn7$F`w$!3=$>(G!*e"fw$Fjn7$Few$!3C`$onS#4$H%Fjn7$Fjw$!3/W?!3B9w"\Fjn7$F_x$!3\ME*fBaHg&Fjn7$Fdx$!3a#ofZ!\S2kFjn7$Fix$!3)R&G%Q;yOL(Fjn7$F^y$!3OO"R%y^uF$)Fjn7$Fcy$!3M9L0nod)o*Fjn7$$"3F+]P%37^j%Fjn$!3\#y2Kyn&R5!#77$Fhy$!34%[7*oi%z6"F_dl7$$"3Sm"z>6but%Fjn$!3%=ZOBAJ<@"F_dl7$F]z$!3k(*fw`Nf=8F_dl7$$"3G+++DM"3%[Fjn$!3tTB%HD#[O9F_dl7$Fbz$!3O`3e&y/Wd"F_dl7$$"3w\7.#Q?&=\Fjn$!3eN'H]K!=f;F_dl7$$"3%)*\(oa-oX\Fjn$!3U-:GC(zLv"F_dl7$$"3#*\PMF,%G(\Fjn$!39%poRKq"f=F_dl7$Fgz$!3W9/xxacz>F_dl-F\[l6#""#F_[l-F$6%7YF+7$$"37+++4x&)*3"F1$"3!e!)e4&*402'F47$$"3*******R2P"Q?F1$"3+dd_A89(4"F17$$"3#)*****pRwX5$F1$"3FYS#Q(G>-;F17$$"3;+++sZ3yTF1$"3qev0'eZn0#F17$$"3M+++]4\Y_F1$"3ETr53m5]CF17$$"3/+++U-/PiF1$"3/vv!p^gnv#F17$$"3G******empisF1$"3,?&))oTN"4IF17$$"3")*****>*>VB$)F1$"3wRA+?ka#>$F17$$"37+++Mbw!Q*F1$"3OOS=e4B(G$F17$$"3++++0j$o/"Fjn$"33A="RLw0G$F17$$"3"******>&>jU6Fjn$"3s#R[$3&)HvJF17$$"31+++j^Z]7Fjn$"3c([095i(GHF17$$"3/+++)=h(e8Fjn$"3dPJ0c))zADF17$$"31+++Q[6j9Fjn$"35t"zdU?V&>F17$$"33+++\z(yb"Fjn$"3wfa:#Go*e7F17$$"3++++b/cq;Fjn$"3^U6Rn*30j"F47$$"3#)*****pJ<gw"Fjn$!3#*R^%4"f_Y5F17$$"3))*****4Mcq(=Fjn$!3Q"HkmrKw'GF17$$"3')*****>pW`(>Fjn$!3=shC8]!Q'\F17$$"3'******4f#=$3#Fjn$!3!HU@-!o3$)zF17$$"3(******>=EX8#Fjn$!3yL`]q&3hx*F17$$"3)******Hxpe=#Fjn$!3Ae(*f2f:(="Fjn7$$"3$)*****RUT%RAFjn$!3yWlAiizY9Fjn7$$"3/+++uI,$H#Fjn$!3)*o:z8Nsh<Fjn7$$"3;+++B3h<BFjn$!3:&[f"fQHI>Fjn7$$"3"******>d3AM#Fjn$!3sF'Gw9#y<@Fjn7$$"3++++Aj!oO#Fjn$!3y\Fj8$=!GBFjn7$$"35+++rSS"R#Fjn$!3)*oX:lw7mDFjn7$$"3&)*****f1OzT#Fjn$!3Ezx&4-;C'GFjn7$$"3#******>1oWW#Fjn$!3;By["3PC@$Fjn7$$"3'*******fStdCFjn$!3qd9y4db8MFjn7$$"3++++e++rCFjn$!3%Qj26$RmOOFjn7$$"3-+++cgE%[#Fjn$!31n)>M6>m)QFjn7$$"33+++`?`(\#Fjn$!3y%es#)=!4qTFjn7$$"3%******fp68^#Fjn$!3zY>&f[o-^%Fjn7$$"38+++S84DDFjn$!3QhWtB^.8\Fjn7$$"3/+++i6)>`#Fjn$!3mX&4;0)\X^Fjn7$$"3)******H)4()QDFjn$!3y%[iX&)GZS&Fjn7$$"3#******R!3wXDFjn$!3)o$)HkDltp&Fjn7$$"3%)*****fi]Eb#Fjn$!3)**[L21oG.'Fjn7$$"3)******p`&4cDFjn$!3Fp%o$pD&3A'Fjn7$$"35+++[/afDFjn$!3]p-Lp0RDkFjn7$$"3))******e`)Hc#Fjn$!3o"\dmQ'e\mFjn7$$"3-+++q-VmDFjn$!3isog-)3v*oFjn7$$"3;+++"=v)pDFjn$!3]fTm;sjurFjn7$$"3%******>4?Ld#Fjn$!3%R%y(o&**f)[(Fjn7$$"35+++-]wwDFjn$!3+![ZPEp/&yFjn7$$"3))*****H"*4-e#Fjn$!3#HUxA\3sF)Fjn7$$"3-+++C[l$e#Fjn$!3#G@d*p.x'z)Fjn7$$"3=+++M(*4(e#Fjn$!35?"G4Uz-Y*Fjn7$$"3%******\kW0f#Fjn$!3iYh;9QyP5F_dl7$$"33+++c&*)Rf#Fjn$!3+.)fw@Zq="F_dl7$$"3')*****pYMuf#Fjn$!3,IzGd**3S;F_dl7$I*undefinedGF&Fegm-F\[l6#""$F_[l-F$6%7OF+7$$"3W*****\a)G\aF4$"3%["eT"f,24$F47$F\gl$"3CPJ"pXkQ1'F47$$"3++++#R(*Rc"F1$"3]4*Q#>1jY&)F47$Fagl$"3Ge(=RE%Q#4"F17$Ffgl$"3y^(oHr\Me"F17$F[hl$"3!\Mu.QA`+#F17$F`hl$"3YeFYaXIMBF17$Fehl$"30ZgLQd$\`#F17$Fjhl$"3VsJ0h=v,EF17$$"3Q*****\KkIz(F1$"3O:0gi.(Gc#F17$F_il$"3[4CJ->()fCF17$$"3k+++l()4_))F1$"3Ul-h$**))zF#F17$Fdil$"3C(z)4v0K&*>F17$$"3E+++!HkX#**F1$"3SNrXN6bl:F17$Fiil$"3uJ^FBV")*R*F47$$"3/+++;_yq5Fjn$"3VHYOh2Y+eF47$$"31+++GTt%4"Fjn$"3!z&=Pq03B:F47$$"32+++SIo=6Fjn$!3dWDD^5x,OF47$F^jl$!3!*=QH-2D;)*F47$$"31+++aB6c6Fjn$!3Q)p8=@(G#R"F17$$"3/+++bFfp6Fjn$!3SzYz_)zw&=F17$$"3-+++cJ2$="Fjn$!3m(QqWUh)*Q#F17$$"3)******zb`l>"Fjn$!3Tf8[WXP0IF17$$"3'*******eR.57Fjn$!3%pdP)>!)yFPF17$$"3%*******fV^B7Fjn$!3YYEoaHM#f%F17$$"3#******4ca-B"Fjn$!31!)f"y%*GU4&F17$$"33+++iZ*pB"Fjn$!3wU)pTS8_l&F17$$"34+++i\tV7Fjn$!3KICB6\"*)G'F17$Fcjl$!3HA#foH!G9qF17$$"3)******>5fQD"Fjn$!3!p/=W*f=@uF17$$"3%*******RICd7Fjn$!3=&3]!e-biyF17$$"31+++ypig7Fjn$!3#\!Gf<")>W$)F17$$"3++++;4,k7Fjn$!3)GD8(e*oN())F17$$"3%******R&[Rn7Fjn$!3mxd/tXPg%*F17$$"3/+++$zy2F"Fjn$!3yJd%o3j<,"Fjn7$$"3'******>tiTF"Fjn$!3'3112*\L'3"Fjn7$$"33+++qmax7Fjn$!3m:9$p!yMs6Fjn7$$"3/+++31$4G"Fjn$!3YDEN7stt7Fjn7$$"3)******fa9VG"Fjn$!3#>=LwA+pR"Fjn7$$"3#******R[)p(G"Fjn$!3Wb)**z(GI`:Fjn7$$"3-+++BC3"H"Fjn$!3[fF"epLow"Fjn7$$"3%******>OmWH"Fjn$!30?$>:R/E5#Fjn7$$"31++++.&yH"Fjn$!3hRE!>auX#HFjnFdgm-F\[l6#""%F_[l-F$6$7$7$"&+D$"%+X7$"&+v$FcdnF[[l-I%TEXTGF%6%7$"&++%FcdnI'k=0.00GF(I+ALIGNRIGHTGF%-F$6$7$7$Fbdn"%+S7$FednFaenFefl-Fgdn6%7$FjdnFaenI'k=0.01GF(F\en-F$6$7$7$Fbdn"%+N7$FednF[fnFfgm-Fgdn6%7$FjdnF[fnI'k=0.02GF(F\en-F$6$7$7$Fbdn"%+I7$FednFefnF[dn-Fgdn6%7$FjdnFefnI'k=0.04GF(F\en-I+AXESLABELSGF%6$Q*Range~(m)F(Q+Height~(m)F(-I&TITLEGF%6#QNEffects~of~Air~Resistance~on~Projectile~RangeF(-I%VIEWGF%6$;F,Fgz;F,$"%+]F-

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

(a) For the situation shown above (n=1) determine the maximum height and range of the object. (b) Repeat problem (a) using v0=500 m/s, for k=0.05 1/s and k=0.15 1/s. Generate a plot showing all three of these solutions on the same graph. (c) For the cases when n=2, find general solutions for both the velocity and position. Create plots of these function using parameters of your own choosing. Expalin the significance and limits of the position function.