# Variable Resistance

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.

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## 1 Answer

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.

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Thanks, amazing what a little shove in the right direction can do. –  PhilCK Feb 16 '11 at 10:13