"If the velocity of a pitched ball has a magnitude of 44.0 m/s and the batted ball's velocity is 58.5 m/s in the opposite direction, find the magnitude of the change in momentum of the ball and of the impulse applied to it by the bat."

An ideal otto cycle has a compression ratio of 10.5, takes in air at 90 kpa and 40°c, and is repeated 2500 times per minute. using constant specific heats at room temperature, determine the thermal efficiency of this cycle and the rate of heat input if the cycle is to produce 90 kw of power.