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

Do you think that this is the correct answer?

enter code heres = NDSolve[{70 y''[t] == -9.8 70 - 0.5 y'[t]*Abs[y'[t]], 
   y[0] == 32000, y'[0] == 0}, y, {t, 0, 100}]
Plot[Evaluate[y[t] /. s], {t, 0, 900}, PlotStyle -> Automatic]

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My opinion is that the parachutist should not have asked his ex-wife to pack his parachute.

As to your equation, your sign convention is mixed up. If you want acceleration to be positive (downward) of 9.8, you can't start at 32000 m. You need to use -9.8. Also, you need y'[t], not y'. I would also use NDSolve to get an answer since its a numerical problem.

Solve the homework problem that way but then think about the terminal velocity of the parachutist (which will prove to be quite terminal for him). See if you can get the same (approximate) answer an easier way using that information.

Regards