1. The total mass of a cyclist and his bicycle is 100 kg .

In all circumstances, the magnitude of the resistance to the motion of the cyclist from non-gravitational forces is modelled as being \(k v ^ { 2 } \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the cyclist. The cyclist can freewheel, without pedalling, down a slope that is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 1 } { 35 }\), at a constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) When he is pedalling up a slope that is inclined to the horizontal at an angle \(\beta\), where \(\sin \beta = \frac { 1 } { 70 }\), and he is moving at the same constant speed \(V \mathrm {~ms} ^ { - 1 }\), he is working at a constant rate of \(P\) watts.

1. Find \(P\) in terms of \(V\). If he pedals and works at a rate of 35 V watts on a horizontal road, he moves at a constant speed of \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
2. Find \(U\) in terms of \(V\).