A man wants to train his son for hitting in professional baseball, but he has a lousy arm and can only throw 42mph. He decides they will train by jumping on board moving trains. His son stands on one train with a bat, and the father stands on a different train and throws the ball at 42mph. They put a base to represent home plate on the train where the son is standing. The father's train is moving at 70mph due East. The son's train is moving at 40mph in the opposite direction along track parallel to the father's (due West). The tracks are separated by 8m.
a) Determine where (how many meters East or West of his son's position) and in what direction the father should throw the ball in order to simulate a big league 110mph fastball that crosses the plate (ignore gravity and solve in 2 dimensions).
b) Determine the velocity of the pitch (speed in mph and direction relative to the tracks) of the ball as observed by someone who is not on either train.
c) If the father's hand is in contact with the ball for 1.4 m, and the ball has a mass of 0.145 kg, how much force must the father exert on average to throw 42mph ?
d) How long does it take for the ball to travel from father to son? Given that, is our decision to ignore gravity reasonable (discuss with numbers)?