A cyclist and his bicycle have a total mass of 90 kg. The cyclist starts to move with speed 3 m s^-1 from the top of a straight hill, of length 500 m, which is inclined at an angle of sin^-1 0.05 to the horizontal. The cyclist moves with constant acceleration until he reaches the bottom of the hill with speed 5 m s^-1. The cyclist generates 420 W of power while moving down the hill. The resistance to the motion of the cyclist and his bicycle, R N, and the cyclist’s speed, v m s^-1, both vary.

1. Show that \(R = \frac{420}{v} + 43.56\).
2. Find the cyclist’s speed at the mid-point of the hill. Hence find the decrease in the value of \(R\) when the cyclist moves from the top of the hill to the mid-point of the hill, and when the cyclist moves from the mid-point of the hill to the bottom of the hill.