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