Answer:
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.
