Take a coordinate system with positive downwards, and corresponding to the parachutists initial position.Originally Posted by askmemath
Now while the parachutist is moving downward the force on here is:
and Newton tells us that so:
or in terms of :
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.
(you will need to check the algebra involved here, and that the assumption
that the parachutists velocity is always positive)