Answer to Question #232462 in Physics for Gian

Question

A 50 kg swimmer dives from a 100 kg boat initially at rest. If the swimmer leaves the boat with a horizontal speed of 2 m/s, find the recoil speed of the boat, neglecting the transfer of momentum to the water.

Answer 1

When they were both at rest, the total momentum of the system was 0. According to momentum conservation, the final total momentum must be 0 as well:

$$p_i=p_f,\\ 0=mv+Mu,\\ mv=-Mu ,\\ 50·2=-100·u,\\ u=-1\text{ m/s}.$$

The minus sign means that the boat moves in the opposite direction.