A woman bails out of an airplane at an altitude of 10,000fts, falls freely for 20s, then open her parachute. How long will it take her to reach the ground? Assume linear air resistance pv ft/s^2, taking p = 0.15 without the parachute and p = 1.5 with the parachute.
My solution so far:
I recognize that Acceleration = gravity - resistance x velocity, since Velocity' = Acceleration, we have v' = g - pv
or dv/dt = 32.2ft - 0.15v
by separation of variables, I obtain V(t), integrating that, I get X(t), the position function.
But in the end, I cannot solve for t in the X(t), since one t is by itself, while I have two ts in the e^.