When baseball players throw the ball in from the outfield, they usually allow it to take one bounce before it reaches the infield, on the theory that the ball arrives sooner that way. Suppose that the angle at which a bounced ball leaves the ground is the same as the angle at which the outfielder threw it, as in Figure P4.55, but that the ball€™s speed after the bounce is one half of what it was before the bounce.
(a) Assuming the ball is always thrown with the same initial speed, at what angle ' 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° with no bounce (green path)?
(b) Determine the ratio of the times for the one-bounce and no-bounce throws.

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45.0 Figure P4.55