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 100.00 mph. Assuming the ball has a mass 143.6 g and has this speed just before a batter would make contact, how much kinetic energy does the ball have?

Kball = _______________ J

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.)

hball = ______________ m

Explanation / Answer

Part I

Mass of the ball is, m = 0.1434 kg

Speed of the ball just before a batter would make contact is, v = 44.694 m/s

Kinetic energy of the ball just before the batter would make contact is,

T = (1/2) m v2

T = 0.5 * 0.1434 * 44.694 * 44.694

T = 143.224595701 J = 143.2246 J

Part II

Acceleration due to gravity is, g = 9.81 m/s2

Let h be the height from which the ball needs to be dropped in order for it to have a potential energy, U = 143.224595701 J

U = mgh = 143.224595701 J

h = 143.224595701 / (0.1434 * 9.81)

h = 101.812111927 m = 101.8121 m is the height from which the ball needs to be dropped in order for it to have a potential energy, U = 143.224595701 J

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