Question

A baseball player uses a pitching machine to help him improve his batting average. He places the 77 kg machine on a frozen pond. The machine fires a 0.153 kg baseball horizontally at a speed of 36.8 m/s. What is the magnitude of the recoil velocity of the machine?

Answer 1

The magnitude of the recoil velocity of the pitching machine is 0.073 m/s, calculated using the law of conservation of momentum and the mass and velocity of the baseball.

Step-by-step explanation:

The student is asking about the conservation of momentum as it applies to a pitching machine firing a baseball and the resulting recoil velocity. According to the law of conservation of momentum, the momentum of the system before and after an event will be the same if no external forces are acting on it. In a scenario where a baseball is projected horizontally, the pitching machine will experience a recoil velocity in the opposite direction.

For the pitching machine (mass M) and baseball (mass m), the initial momentum of the system is 0 because they are both at rest. After the baseball is fired, the conservation of momentum is given by:

• Initial total momentum = Final total momentum
• 0 = (mass of baseball × velocity of baseball) + (mass of machine × recoil velocity of machine)
• 0 = m × v + M × V
• Recoil velocity of machine (V) = -(m × v)/M

Plugging in the given values:

Recoil velocity of machine = -(0.153 kg × 36.8 m/s) / 77 kg

Recoil velocity of machine = -0.073 m/s (negative sign indicates opposite direction)

The magnitude of the recoil velocity is the absolute value:

Recoil velocity of machine = 0.073 m/s