A baseball player uses a pitching machine to help him improve his batting average. He places the 67.1 kg machine on a frozen pond. The machine fires a 0.101 kg baseball horizontally at a speed of 32.6 m/s. What is the magnitude of the recoil velocity of the machine

The magnitude of the recoil velocity of the machine is 0.05  m/s.

Explanation:

Given;

mass of the baseball, m₁ = 0.101 kg

mass of the machine, m₂ = 67.1 kg

velocity of the baseball, v₁ = 32.6 m/s

let v₂ be the recoil velocity of the machine.

Apply the principle of conservation of linear momentum; the total momentum before and after firing the ball must be constant.

sum of the initial momentum of the ball and the machine = 0  (at rest)

sum of the final momentum of the ball and the machine = m₁v₁ + m₂v₂

Since total momentum is constant; m₁v₁ + m₂v₂ = 0

m₁v₁ + m₂v₂ = 0

(0.101 x 32.6) + (67.1)v₂ = 0

67.1v₂ = -3.2926

v₂ = (-3.2926) / 67.1

v₂ = -0.05  m/s (the negative sign shows that it is the opposite direction)

Thus, the magnitude of the recoil velocity of the machine is 0.05  m/s.

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