Serway & Jewett — Motion in Two Dimensions: Problem 46

An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in Figure P4.46, but that the ball’s speed after the bounce is one-half of what it was before the bounce. (a) Assume the ball is always thrown with the same initial speed and ignore air resistance. At what angle \(\theta\) should the fielder throw the ball to make it go the same distance \(D\) with one bounce (blue path) as a ball thrown upward at \(45.0^{\circ}\) with no bounce (green path)? (b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.