# Math Help - Acceleration-Velocity Models problem

1. ## Acceleration-Velocity Models problem

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^.

Any help?

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^.

Any help?
That's correct. You have a displacement function of the form
$x(t) = at + be^{-ct}$
(a, b, and c, are just constants. a is not meant to represent acceleration.)

Probably the best way to solve this is by a "successive guess" technique: see if you can find a t such that x = 10000 ft.

-Dan