Question

1. Assume that in the process of throwing a baseball pitch, the baseball leaves the hand of the pitcher 6 vertical feet above and 60 horizontal feet from home plate. Also assume that your coordinate axes are such that the origin is at ground level directly below the point of release. (a) On the first pitch, the pitcher throws a 140 ft/sec (≈ 95 mph) fastball directly at the center of the strike zone. In the absence of all forces except gravity, how far above the ground is the ball when it crosses home plate and how long does it take the pitch to arrive? (b) A simple model to describe the curve of a baseball assumes the spin of the ball produces a constant sideways acceleration (in our case, the y−direction) of c ft/s2 . Suppose for the second pitch the pitcher throws a curveball with c = 8 ft/s2 . How far does the ball move in the y−direction by the time it reaches home plate, assuming an initial velocity of 117 ft/s? (c) Given that the average strike zone is extends approximately 1.5 feet from the ground up to 3.5 feet above the ground and is approximately 1.5 feet wide (centered over homeplate), were these 2 pitches strikes? (d) In part (b), does the ball curve more in the first half of its trip to the plate or in the second half? Justify your answer. This is everything the question gives.

Answer 1