Take a coordinate system with positive downwards, and corresponding to the parachutists initial position.Originally Posted byaskmemath

Now while the parachutist is moving downward the force on here is:

and Newton tells us that so:

or in terms of :

,

rearranging gives:

.

Now this may be solved in the usual manner, the solution the sum of a

solution to the homogeneous equation:

and a particular integral of the original equation.

For the homogeneous equation, try a solution of the form , then:

,

which has solutions and , so the general solution to HE is:

.

Now a particular integral of the original DE is the constant velocity solution:

so the PI is:

,

so the general solution is:

Now at we have so .

Also gives , so the solution is:

.

Which is sufficient to answer the questions asked.

RonL

(you will need to check the algebra involved here, and that the assumption

that the parachutists velocity is always positive)