I'm stuck on this question from a past paper.
A parachutist jumps out of a hot air balloon. The resistance is proportional to the speed of the parachutist. The parachutist has a terminal velocity of 4 ms-1
How far did he fall after 3 seconds.
I'm really not sure how to go about this question, any help much appreciated.
The downward acceleration in the absence of resistance is g, and you are told there is an upward force proportional to speed. So (letting primes be d/dt) z"=-g+kz' where k is the constant of proportionality between speed and resistance. The terminal velocity lets you figure k, then you integrate the equation with respect to t.
