Question

The speed of the fastest-pitched baseball was 43.0 m/s , and the ball's mass was 145 g .

How fast would a 54.0 gram ball have to travel to have the same amount of kinetic energy?

v =

67.9867.98

  m/s  

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Part D

How fast would a 54.0 gram ball have to travel to have the same amount of momentum?

v =

107.5107.5

  m/s  

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Answer 1

Mass of the baseball = m₁ = 145 g = 0.145 kg

Speed of the baseball = V₁ = 43 m/s

Kinetic energy of the baseball = KE₁

KE₁ = m₁V₁²/2

KE₁ = (0.145)(43)²/2

KE₁ = 134.05 J

Momentum of the baseball = P₁

P₁ = m₁V₁

P₁ = (0.145)(43)

P₁ = 6.235 kg.m/s

Mass of the second ball = m₂ = 54 g = 0.054 kg

Speed of the 54 g ball to have the same kinetic energy as the baseball = V₂

KE₁ = m₂V₂²/2

134.05 = (0.054)V₂²/2

V₂ = 70.46 m/s

Speed of the 54 g ball to have the same momentum as the baseball = V₃

P₁ = m₂V₃

6.235 = (0.054)V₃

V₃ = 115.46 m/s

a) Speed of the 54 g ball to have the same kinetic energy as the baseball = 70.46 m/s

b) Speed of the 54 g ball to have the same momentum as the baseball = 115.46 m/s