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MathGroup Archive 2005

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NDSolve and InterpolatingFunction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56095] NDSolve and InterpolatingFunction
  • From: Virgil Stokes <virgil.stokes at it.uu.se>
  • Date: Fri, 15 Apr 2005 04:47:41 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I am solving the following system of ODE's

   g = 9.81 ; (* acceleration of gravity [m/s^2] *)
   d = 0.063; (* diameter of ball [m] *)
   m = 0.05; (* mass in kg *)
   \[Rho] = 1.29; (* air density, [kg/m^3] *)
   \[Alpha] = \[Rho]  Pi  d^2/(8  m)

   h = 1; (* initial height [m] *)
   v0 = 25; (* magnitude of ball velocity [m/s] *)
   \[Theta] = 15  (* initial angle of release [15 degrees] *)

   vars = {x[t], vx[t], z[t], vz[t]}

   initc = {x[0] == 0, vx[0] == v0*Cos[\[Theta] Degree], z[0] == h,
    vz[0] == v0*Sin[\[Theta] Degree]}

   v[t] = Sqrt[vx[t]^2 + vz[t]^2];

   eq1  = x'[t] == vx[t];
   eq2 = vx'[t] == -0.508 \[Alpha] vx[t] v[t];
   eq3 = z'[t] == vz[t];
   eq4 = vz'[t] == -g - 0.508 \[Alpha] vz[t] v[t];
   eqns = {eq1, eq2, eq3, eq4}

   sol = NDSolve[Join[eqns, initc], vars, {t, 0, 25}]

which works fine; but how can I find (e.g. using Solve) the value of t 
such that z[t] is 0; i.e, where, z[t] (in the
form of an InterpolatingFunction) is zero.

--V. Stokes


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