6 A cyclist is cycling with constant power of 160 W along a horizontal straight road. There is a constant resistance to motion of 20 N . At an instant when the cyclist's speed is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), his acceleration is \(0.15 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Show that the total mass of the cyclist and bicycle is 80 kg . The cyclist comes to a hill inclined at \(2 ^ { \circ }\) to the horizontal. When the cyclist starts climbing the hill, he increases his power to a constant 300 W . The resistance to motion remains 20 N .
2. Show that the steady speed up the hill which the cyclist can maintain when working at this power is \(6.26 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to 3 significant figures.
3. Find the acceleration at an instant when the cyclist is travelling at \(90 \%\) of the speed in part (ii).