4. The resistance to the motion of a cyclist is modelled as \(k v ^ { 2 } \mathrm {~N}\), where \(k\) is a constant and \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the cyclist. The total mass of the cyclist and his bicycle is 100 kg . The cyclist freewheels down a slope inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 20 }\), at a constant speed of \(3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(k = 4\). The cyclist ascends a slope inclined at an angle \(\beta\) to the horizontal, where \(\sin \beta = \frac { 1 } { 40 }\), at a constant speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Find the rate at which the cyclist is working.
   (6 marks)