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MathGroup Archive 2007

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Re: Projectile motion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79882] Re: Projectile motion
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 8 Aug 2007 04:44:18 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <f9912q$c4n$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

a) it is not wise to solve the ode every time even when the
    analytical solution can be found and the time where the ball
    hit the ground is known to be
     2 v Sin[Theta]/g
b)

Manipulate[
  Module[{eqns, soln, x, y, t},
   eqns = {x'[t] == v Cos[Theta], x[0] == 0,
     y'[t] == -g t + v Sin[Theta], y[0] == 0};
   soln = Flatten[NDSolve[eqns, {x, y}, {t, 0, 2 v Sin[Theta]/g}]];
   With[{d = x[p] /. soln, h = y[p] /. soln},
    Graphics[{Blue, Disk[{d, h}, .2]},
     PlotRange -> {{-.5, 12}, {-.5, 6}}, Frame -> True,
     PlotLabel ->
      TableForm[{"Theta =" <>
         ToString[NumberForm[Theta 180/Pi, {2, 0}]],
        "vx =" <> ToString[NumberForm[Chop[N[v Cos[Theta]]], {2, 1}]],
        "vy =" <> ToString[NumberForm[Chop[N[v Sin[Theta]]], {2, 1}]],
        "xmax =" <>
         ToString[NumberForm[N[(v2 Sin[2 Theta])/g], {3, 2}]],
        "ymax =" <>
         ToString[
          NumberForm[N[(v Sin[Theta]) 2/(2 g)], {3, 2}]]}]]]], {{v, 5,
    "Initial Velocity"}, 1, 10}, {{g, 9.8, "Gravitational Constant"},
   0, 30}, {{Theta, Pi/4, "Theta"}, 0, Pi/2}, {{p, 0, "Animate"}, 0,
   2 v Sin[Theta]/g, ControlType -> Trigger}]

will do that.

Regards
   Jens


Mike wrote:
> All:
> 
> I'd like to be able to stop the "disk" when it arrives at xmax. Can anyone give me a hint?
> 
> Thx,
> 
> Mike
> 
> 
> Manipulate[
>  Module[{eqns, soln, x, y, t}, 
>   eqns = {x'[t] == v Cos[Theta], x[0] == 0, 
>     y'[t] == -g t + v Sin[Theta], y[0] == 0}; 
>   soln = Flatten[NDSolve[eqns, {x, y}, {t, 0, p}]]; 
>   With[{d = x[p] /. soln, h = y[p] /. soln}, 
>    Graphics[{Blue, Disk[{d, h}, .2]}, 
>     PlotRange -> {{-.5, 12}, {-.5, 6}}, Frame -> True, 
>     PlotLabel -> 
>      TableForm[{"Theta =" <> 
>         ToString[NumberForm[Theta 180/Pi , {2, 0}]], 
>        "vx =" <> 
>         ToString[NumberForm[Chop[N[v Cos[Theta]]] , {2, 1}]], 
>        "vy =" <> 
>         ToString[NumberForm[Chop[N[v Sin[Theta]]] , {2, 1}]], 
>        "xmax =" <> 
>         ToString[NumberForm[N[(v^2 Sin[2 Theta])/g] , {3, 2}]], 
>        "ymax =" <> 
>         ToString[
>          NumberForm[N[(v Sin[Theta])^2/(2 g)] , {3, 2}]]}]]]], {{v,
>     5, "Initial Velocity"}, 1, 
>   10}, {{g, 9.8, "Gravitational Constant"}, 0, 
>   30}, {{Theta, Pi/4 , "Theta"}, 0, Pi/
>   2}, {{p, 0, "Animate"}, 0, 2, ControlType -> Trigger}]
> 


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