Question

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 1

0.103 m/s to the south

Step-by-step explanation:

The total momentum of the launcher+ball system must be conserved before and after the launch, so we can write:

`p_i = p_f\\0 = m_L v_L + m_B v_B`

where

`p_i =0` is the total initial momentum (before the launch)

`m_L = 20 kg` is the mass of the launcher

`v_L` is the velocity of the launcher after the launch

`m_B = 0.057 kg` is the mass of the ball

`v_B = +36 m/s` is the velocity of the ball after the launch (we take the north direction as positive)

Solving for
`v_L`, we find

`v_L = -(m_B v_B)/(m_L)=-((0.057 kg)(+36 m/s))/(20 kg)=-0.103 m/s`

and the negative sign means that the direction is south.