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 44.47 m/s (99.50 mph). Assuming the ball has a mass 0.1440 kg 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

Kball = 0.5*m*v^2 = 0.5*0.144*44.47*44.47 = 142.38 m/s

to attain the same energy ,or the same speed the ball should be droped from

a height h_ball

then v = sqrt(2*g*h_ball)

44.47^2 = 2*9.81*h_ball

h_ball = 44.47*44.47/(2*9.81) = 100.8 m

(or )

apply law of conservation of energy

energy at the highest point = energy at the bottom

m*g*h_ball = 142.38

h_ball = 142.38/(m*g) = 142.38/(0.144*9.81) = 100.8 m

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