Answer:
0.103 m/s to the south
Explanation:
The total momentum of the launcher+ball system must be conserved before and after the launch, so we can write:
[tex]p_i = p_f\\0 = m_L v_L + m_B v_B[/tex]
where
[tex]p_i =0[/tex] is the total initial momentum (before the launch)
[tex]m_L = 20 kg[/tex] is the mass of the launcher
[tex]v_L[/tex] is the velocity of the launcher after the launch
[tex]m_B = 0.057 kg[/tex] is the mass of the ball
[tex]v_B = +36 m/s[/tex] is the velocity of the ball after the launch (we take the north direction as positive)
Solving for [tex]v_L[/tex], we find
[tex]v_L = -\frac{m_B v_B}{m_L}=-\frac{(0.057 kg)(+36 m/s)}{20 kg}=-0.103 m/s[/tex]
and the negative sign means that the direction is south.
