Professional baseball pitchers can deliver a pitch which can reach the blazing s

Question

Professional baseball pitchers can deliver a pitch which can reach the blazing speed of 100 mph (miles per hour). A local team has drafted an up-and-coming left handed pitcher who can consistently throw at 99.00 mph. Assuming the ball has a mass 144.0 g and has this speed just before a batter would make contact, how much kinetic energy does the ball have? How high would the ball need to be dropped from to attain the same energy (neglect air resistance)? (The acceleration due to gravity is 9.81 m/s2.)

Explanation / Answer

Kinetic energy = 0.5 mv^2

where m = mas sof ball = 144g = 0.144 kg

v = speed of ball = 99.00 mph = 44.26 m/s

Kinetic energy = 0.5(0.144)(44.26)^2 = 141 J

To attain the same kinetic energy, ball must have same potential energy before being dropped

Potential energy = kinetic energy = 141 J

mgh = 141 J where g = acceleration due to gravity = 9.81 m/s^2 and h = height

(0.144)(9.81)h = 141

h = 99.8 m

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