M2 January 2010 Q5

5. A cyclist and her bicycle have a total mass of 70 kg. She cycles along a straight horizontal road with constant speed 3.5 m s\(^{-1}\). She is working at a constant rate of 490 W.

The cyclist now cycles down a straight road which is inclined at an angle \(\theta\) to the horizontal, where \(\sin\theta = \dfrac{1}{14}\), at a constant speed \(U\) m s\(^{-1}\). The magnitude of the non-gravitational resistance to motion is modelled as \(40U\) newtons. She is now working at a constant rate of 24 W.