10 3. The total mass of a cyclist and his bicycle is 100 kg. In all circumstances, the magnitude of the resistance to the motion of the cyclist from non-gravitational forces is modelled as being kv2 N, where v m s−1 is the speed of the cyclist. The cyclist can freewheel, without pedalling, down a slope that is inclined to the horizontal at an angle α, where sin α = 1 35 , at a constant speed of V m s−1 When he is pedalling up a slope that is inclined to the horizontal at an angle β, where sin β = 1 70 , and he is moving at the same constant speed V m s−1 , he is working at a constant rate of P watts. (a) Find P in terms of V. (7) If he pedals and works at a rate of 35 V watts on a horizontal road, he moves at a constant speed of U m s−1 (b) Find U in terms of V. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________