Differential Equations using velocity

Here is my problem:

The equation:

describes the velocity v of a parachute jumper. We have and .

1. Solve. I found .

2. Find v(t) as . I found .

3. When is dv/dt the largest? At that moment, how many G's of force does the jumper experience? It is largest at t=0 at by replace the value of v at t=0 in the expression of dv/dt, I find dv/dt=-30. Therefore the jumper experiences 3G of force.

4. Here I am having trouble. If an auxiliary parachute opens at time , the coefficient K=K(t) is .

Without solving this new equation, figure out a reasonable choice for the constant so that the parachutist is not subject to worse $G$ forces that already exerted, but at the same time allows for the softest landing. With this choice of , find the landing speed v (again without solving the equations).

Thank you in advance

Re: Differential Equations using velocity