7 A parachutist of mass \(m \mathrm {~kg}\) opens his parachute when he is moving vertically downwards with a speed of \(50 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(t \mathrm {~s}\) after opening his parachute, he has fallen a distance \(x \mathrm {~m}\) from the point where he opened his parachute, and his speed is \(v \mathrm {~ms} ^ { - 1 }\). The forces acting on him are his weight and a resistive force of magnitude \(m v \mathrm {~N}\).

1. Find an expression for \(v\) in terms of \(t\).
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2. Find an expression for \(x\) in terms of \(t\).
3. Find the distance that the parachutist has fallen, since opening his parachute, when his speed is \(15 \mathrm {~ms} ^ { - 1 }\).
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