How to Calculate Velocity of Tennis Ball Launcher

What is the velocity of the tennis ball launcher after the launch?

Given data: A 20kg tennis ball launcher shoots a 0.057kg tennis ball across a frictionless court. If the tennis ball's velocity after it is launched is 36m/s to the north, what is the velocity of the tennis ball launcher?

Answer:

The velocity of the tennis ball launcher after the launch is 0.103 m/s to the south.

When calculating the velocity of the tennis ball launcher after launch, we need to apply the principle of conservation of momentum. In this scenario, the total momentum of the launcher and the ball system must be conserved both before and after the launch.

We can set up the equation as follows:

Total initial momentum (before the launch) = Total final momentum (after the launch)

0 = m_L*v_L + m_B*v_B

Where:

m_L = 20 kg (mass of the launcher)

v_L = velocity of the launcher after the launch

m_B = 0.057 kg (mass of the ball)

v_B = +36 m/s (velocity of the ball after the launch in the north direction)

Solving for v_L:

v_L = -m_B*v_B/m_L

= -(0.057 kg)*(+36 m/s)/20 kg

= -0.103 m/s

The negative sign indicates that the velocity of the tennis ball launcher after the launch is 0.103 m/s to the south.