A 0.32 lb baseball crosses the plate at 94 mph. If the batter hits the ball back toward the pitcher at 126 mph, use impulse and momentum equations to find the force of the bat on the ball, given that the ball contacts the bat for 0.0015 seconds.

Note: You may need to consider unit conversions, such as 1 mile = 5280 feet.

Mass of baseball = 0.32 lb Initial velocity of baseball = 94 mph = (94 × 5280) / 3600 = 138.67 ft/s Final velocity of baseball = 126 mph = (126 × 5280) / 3600 = 184.8 ft/s Time taken by baseball to come to rest = 0.0015 s Force of the bat on the ball = Formulae to be used: Impulse = Change in momentum Force × time = Change in momentum. Momentum of the ball before being hit by the bat, p1 = mv1 = 0.32 × 32.17 × 138.67= 1453.25 lb ft/s Momentum of the ball after being hit by the bat, p2 = mv2 = 0.32 × 32.17 × 184.8= 1962.48 lb ft/s Change in momentum, ∆p = p2 – p1= 1962.48 – 1453.25= 509.23 lb ft/s Impulse = Change in momentum = ∆p= 509.23 lb ft/s Force × time = ∆p Force = ∆p / time = 509.23 / 0.0015= 339486.67 lb

The force of the bat on the ball is 339486.67 lb.

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