A 750 kg hammer is used to drive a 2500 kg pile into some loosely packed sand. The hammer is released from a height of 2.5 m above the top of the pile and is seen to rebound to a maximum height of 0.15 m above the point of impact. Determine: (a) the velocity of the pile immediately after impact, (b) the coefficient of restitution, and (c) the average force exerted by the hammer on the pile if the impact takes place over 0.08 s.