Question: A parachutist jumps from a hot air balloon. The parachute opens immediately and the air resistance with the parachute opens is proportional to the speed of the parachutist. The terminal speed is \(4 \mathrm{~ms}^{-1}\). Determine the distance the parachutist drops in the first (i) \(2 \mathrm{sec}\) and (ii) 10 sec of descent.

Hint: Use the result in Example 2 for the velocity $v$ as a function of $t$ and then integrate to obtain the distance $x$ fallen as a function of $t$.

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