4 The total mass of a cyclist and her bicycle is 70 kg . The cyclist is riding with constant power of 180 W up a straight hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.05\). At an instant when the cyclist's speed is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), her acceleration is \(- 0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). There is a constant resistance to motion of magnitude \(F \mathrm {~N}\).

1. Find the value of \(F\).
2. Find the steady speed that the cyclist could maintain up the hill when working at this power. [2]