A tennis player places a 54 kg ball machine on a frictionless surface. The machine fires a 0.057 kg tennis ball horizontally with a velocity of 38 m/s toward the north. What is the final velocity of the machine?
m/s to the south
To find the final velocity of the machine, we need to use the principle of conservation of momentum. The momentum before the tennis ball is fired is equal to the momentum after the tennis ball is fired.
The momentum before the tennis ball is fired can be calculated using the formula:
Initial momentum = (mass of ball machine) × (initial velocity of ball machine)
Given:
Mass of ball machine = 54 kg
Initial velocity of ball machine = 0 m/s (since it is at rest before firing the tennis ball)
Initial momentum = (54 kg) × (0 m/s) = 0 kg·m/s
The momentum after the tennis ball is fired is the sum of the momenta of the ball machine and the tennis ball.
The momentum of the tennis ball can be calculated using the formula:
Momentum of tennis ball = (mass of tennis ball) × (final velocity of tennis ball)
Given:
Mass of tennis ball = 0.057 kg
Final velocity of tennis ball = 38 m/s (toward the north)
Momentum of tennis ball = (0.057 kg) × (38 m/s) = 2.166 kg·m/s
Now, we can find the final velocity of the machine by rearranging the formula for momentum and solving for the final velocity:
Final velocity of ball machine = (momentum before - momentum of tennis ball) / (mass of ball machine)
Final velocity of ball machine = (0 kg·m/s - 2.166 kg·m/s) / (54 kg) = -0.040 m/s (southward)
Therefore, the final velocity of the machine is -0.040 m/s to the south.