1. Assume that in the process of throwing a baseball pitch, thebaseball leaves the hand of the pitcher 6 vertical feet above and60 horizontal feet from home plate. Also assume that yourcoordinate axes are such that the origin is at ground leveldirectly below the point of release. (a) On the first pitch, thepitcher throws a 140 ft/sec (≈ 95 mph) fastball directly at thecenter of the strike zone. In the absence of all forces exceptgravity, how far above the ground is the ball when it crosses homeplate and how long does it take the pitch to arrive? (b) A simplemodel to describe the curve of a baseball assumes the spin of theball produces a constant sideways acceleration (in our case, they−direction) of c ft/s2 . Suppose for the second pitch the pitcherthrows a curveball with c = 8 ft/s2 . How far does the ball move inthe y−direction by the time it reaches home plate, assuming aninitial velocity of 117 ft/s? (c) Given that the average strikezone is extends approximately 1.5 feet from the ground up to 3.5feet above the ground and is approximately 1.5 feet wide (centeredover homeplate), were these 2 pitches strikes? (d) In part (b),does the ball curve more in the first half of its trip to the plateor in the second half? Justify your answer. This is everything thequestion gives.
