Question

Two campers dock a canoe. One camper steps onto the dock.  This camper has a mass of 80 kg and moves forward at 4.0 m/s. With what speed and direction do the canoe and the other camper move if their combined mass is 110 kg?

Answer 1

According to the momentum conservation law, the momentum $p_1$ of the first camper is equal to the momentum $p_2$ of the boat with the second camper. By definition, the momentums are given as follows:

$$p_1 = m_1v_1\\ p_2 = m_2v_2$$

where $m_1 = 80kg, m_2 = 110kg$ are the masses of the first camper, and the boat with the second camper respectively, $v_1 = 4m/s,v_2$ are the speeds of the first camper, and the boat with the second camper respectively.

Thus, obtain the equality:

$$m_1v_1 = m_2v_2\\ v_2 = \dfrac{m_1v_1 }{m_2} = \dfrac{80kg\cdot 4m/s}{110kg} \approx 2.9m/s$$

The direction of this velocity is opposite to the direction of $v_1$ (thus, backward).

Answer. 2.9 m/s backward.