A differential thermocouple with sensors at the inlet and the exit of a pump indicates that the temperature of water rises 0.048°f as it flows through the pump at a rate of 1.5 ft3/s. if the shaft power input to the pump is 21.6 hp and the heat loss to the surrounding air is negligible, determine the mechanical efficiency of the pump.

In a game of pool, ball a is moving with a velocity v0 of magnitude v0 = 15 ft/s when it strikes balls b and c, which are at rest and aligned as shown. knowing that after the collision the three balls move in the directions indicated and assuming frictionless surfaces and perfectly elastic impact (that is, conservation of energy), determine the magnitudes of the velocities va, vb, and vc.