Improving Batting Average with Pitching Machine
How does a baseball player use a pitching machine to improve batting average?
A baseball player uses a pitching machine to help him improve his batting average. He places the 54.6 kg machine on a frozen pond. The machine fires a 0.149 kg baseball horizontally at a speed of 42.6 m/s. What is the magnitude of the recoil velocity of the machine?
Understanding the Law of Conservation of Momentum
The law of conservation of momentum states that when two or more bodies are operating upon each other in an isolated system, their combined momentum remains constant unless an external force is applied. This means momentum cannot be created or destroyed.
The mass of the pitching machine is 54.6 kg.
The mass of the baseball is 0.149 kg.
The velocity of the baseball is 42.6 m/s.
To find the recoil velocity of the machine, we can use the principle of conservation of momentum.
Calculating Recoil Velocity of the Machine
According to the law of conservation of momentum, the momentum of the machine is equal in magnitude but opposite in direction to the momentum of the ball.
Using the formula MV = -mv (where M is the mass of the machine, V is the recoil velocity of the machine, m is the mass of the baseball, and v is the velocity of the baseball):
V = -mv/M
V = - (0.149 × 42.6) / 54.6 m/s
V = - 0.11 m/s
Therefore, the recoil velocity of the machine is 0.11 m/s in the opposite direction.
By understanding the law of conservation of momentum, we can see how the interaction between the pitching machine and the baseball results in the recoil velocity that helps the baseball player improve his batting average.