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A 5\frac { 1 }{ 8 } oz baseball traveling at 80 mph rebounds off a bat with a speed of 160 mph. The ball is in contact with the bat for roughly { 10 }^{ -3 } s. The incoming velocity of the ball is horizontal, and the outgoing trajectory forms an angle \alpha =31° angle with respect to the incoming trajectory.
(a) Determine the impulse provided to the baseball by the bat.
(b) Determine the average force exerted by the bat on the ball.
(c) Determine how much the angle \alpha would change (with respect to 31°) if we
were to neglect the effects of the force of gravity on the ball.

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