A cyclist and her bicycle have a combined mass of 75 kg. She comes to a complete stop at the crest of 15 m high hill, then coast down the hill without pedalling.

Question

a) Calculate her speed at the bottom of the hill.
b) Calculate her speed if she does not stop and coast, but continues pedalling her bike at 5 m/s to the bottom.
c) What would happen to her speed at the bottom of the hill if it were twice as steep?

Answer 1

m g h = (1/2) m v^2
so
v^2 = 2 g h = 2 * 9.81 * 15 = 294.3
v = 17.2 m/s

Well, if she keeps going 5 m/s then her speed does not change but I think it means she has initial speed of 15 V
kinetic energy at 15 = (1/2) m (225)
so total energy at base = (1/2) m (225) + m g h
so
(1/2) v^2 = 225/2 + g h
v^2 =225 + 294.3 = 519.3
v = 22.8 m/s

nothing if height the same.