A firefighter stands on a stationary boat floating on a calm lake. The firefighter jumps horizontally off the front of the boat onto a jetty. Explain why the boat moves backwards as the firefighter jumps forwards. Your answer must refer to momentum.

Before the jump the firefighter and the boat are stationary, so the total momentum of the system is zero.

When the firefighter jumps forwards, his momentum becomes
(p_{ ext{firefighter}} = m_{ ext{firefighter}};v_{ ext{firefighter}}) in the forward direction.

Because no external horizontal forces act on the system, momentum is conserved. Therefore the boat must acquire an equal and opposite momentum:
(p_{ ext{boat}} = -p_{ ext{firefighter}}) in the backward direction.

Since the boat’s mass (120 kg) is much larger than the firefighter’s mass, the boat’s speed (v_{ ext{boat}} = p_{ ext{boat}}/m_{ ext{boat}}) is much smaller than the firefighter’s speed. Hence the boat moves backwards slowly while the firefighter moves forwards.