physics

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When baseball players throw the ball in from the outfield, they sometimes allow it to take one bounce before it reaches the infield on the theory that the ball arrives sooner that way. Suppose the angle at which a bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but the ball’s speed after the bounce is ½ of what it was before the bounce. (a) Assume the ball is always thrown with the same initial speed. At what angle θ should the fielder throw the ball to make it go the same distance D with one bounce as a ball thrown upward at 45.0o with no bounce? (b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw (t of bounced ball / t of 45o ball)

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