       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, vx == v0*Cos[\[Theta] Degree], z == h,
vz == 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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