My only correction is that you ended the NDSolve too early (100 vs 900 seconds).
s = NDSolve[{70 y''[t] == -9.8 70 - 0.5 y'[t]*Abs[y'[t]],
y[0] == 32000, y'[0] == 0}, y, {t, 0, 900}]
You can find the intercept with
Solve[(y /. s)[[1]][t] == 0, t]
I think the problem is to make you realize that the velocity very quickly reaches terminal velocity and stays constant for most of the fall. You can use this fact to solve the problem. You can calculate the terminal velocity by setting y''[t] to zero and solve for y'[t]. You can calculate the time to accelerate to terminal velocity and add on the time to fall that distance at that velocity. All this can be done without solving a single differential equation.
Regards