9709 P42 - Mar 2022 - Q4
3492
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 m s\(^{-1}\), her acceleration is \(-0.2 \text{ m s}^{-2}\). There is a constant resistance to motion of magnitude \(F \text{ N}\).
(a) Find the value of \(F\).
(b) Find the steady speed that the cyclist could maintain up the hill when working at this power.
