Question

A boy holding on to some support throws a stone horizontally with a velocity of 5 m/sec. (a) What velocity could he impart to the stone if he were to throw it with the previous force, expending the same amount of energy, while standing on skates on smooth ice? The mass of the stone is 1kg and the mass of the boy is 49 kg. (b) Does the boy develop the same power in both cases? (c) What is the velocity of the stone relative to the boy in the second case?  

Answer 1

In the first case the boy does an amount of work

A = 1/2(mv₁²).

in throwing the stone. If in the second case he throws the stone with the same force, doing the same amount of work, the latter is expended in imparting kinetic energy to the stone and to the boy himself. Therefore

where u is the velocity of the boy. According to the law of conservation of momentum,

Since the power is given by N = Fv and since, in the second case, the stone moves faster relative to the boy than in the first case, (v > v₁), the boy should develop a greater power in the second case.