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Laws of Motion/Free Fall

Question: 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, but that the ball's speed after the bounce is one half what it was before the bounce.

(a) Assuming that the ball is always thrown at the same initial speed, at what angle should the outfielder throw the ball to make it go the same distance D with one bounce, as a ball thrown at the initial angle, with no bounce?
(b) Determine the ratio of times for the one-bounce and no-bounce throws.

Solution Preview

a.) Because range of projectile motion is given as: R = u^2*sin(2*theta)/g
For no bounce, theta = 45 degrees
R(no bounce) = u^2*sin(2*45)/g = u^2/g (1)

For one-bounce:
R(one bounce) = [u^2*sin(2*theta)/g] + ...

Solution Summary

This solution provides a fully, completed response to this problem pertaining to physics mechanics, which includes the required formulas and a breakdown of how to work through each formula to produce the answer.