speed question- physics

Question

A baseball player swings a 4 kg bat at 49.3 m/s to hit a line drive ball (0.57 kg) right back to the pitcher. The baseball was initially pitched at 32.9 m/s and flies back towards the pitcher at 46 m/s. What is the bat speed after hitting the ball? Report your answer to 0.1 m/s. Assume that towards the pitcher is positive.

Give your answer with one decimal.

 

thank you! :)

Answer 1

Use conservation of linear momentum.

 

m = mass of ball = 0.57 kg

u₁ = initial speed of ball = -32.9 m/s

u₂ = final speed of ball = 46 m/s

 

M = mass of bat = 4kg

v₁ = initial speed of bat = 49.3 m/s

v₂ = final speed of bat = ?

 

mu₁ + Mv₁ = mu₂ + Mv₂

 

Mv₂ = mu₁ - mu₂ + Mv₁ = Mv₁ + m(u₁ - u₂) 

 

v₂ = v₁ + (m/M)(u₁ - u₂) = [49.3 + (0.57/4)(-32.9 - 46)] m/s ≅ 38.1 m/s

 

v₂ ≅ 38.1 m/s