Question

Mark, a 65.0 kg skin diver, shoots a 4.0 kg spear with a speed of 25 m/s at fish who darts quickly away without getting hit. How fast does Mark move backwards when the spear is shot?

Answer 1

The speed can be found from momentum conservation:

$$0=m_sv_s+m_Mv_M,\\\space\\ v_M=-v_s\frac{m_s}{m_M}=-1.54\text{ m/s}.$$