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I want to know exact x'[t] value where z[t]=0

I know approximate x'[t] value is 107

but I cannot find how to find exact x'[t] value

    (*1 mph = 0.44704 m/s
    50000ft=15240m*)

    g = 9.81;
    {d, Subscript[c, 1], Subscript[c, 2]} = {0.2 2, 1.55 10^-4 d, 0.22 d^2};
    mass = 100;

    ls0 = NDSolve[{x''[t] + Subscript[c, 2]/mass ((x'[t] + 26.8)^2 + z'[t]^2)^(1/2) (x'[t] + 26.8) == 0, z''[t] + Subscript[c, 2]/mass ((x'[t] + 26.8)^2 + z'[t]^2)^(1/2) z'[t] + g == 0, z[0] == 15240, z'[0] == 0, x'[0] == 107, x[0] == 0}, {x, z}, {t, 0, 1000}]

ParametricPlot[
Evaluate[{x[t], z[t]} /. ls0], {t, 0, 110}, PlotRange -> All, AxesLabel -> {speed, flying altitude}, AspectRatio -> 1/GoldenRatio]

enter image description here

enter image description here

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You're using a numerical method.... What do you mean by "exact"? –  belisarius Jul 8 at 4:24
    
I know What you mean.. But I don't know how to code numerically What I want –  user16336 Jul 8 at 4:37

1 Answer 1

up vote 0 down vote accepted
t0 = t /. First@N@Solve[{Evaluate[z[t] /. ls0] == 0}, t]

104.606

z[t0] /. ls0

{-7.25357*10^-13}

x'[t0] /. ls0

{-26.3732}

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