Answer to Question #151373 in Classical Mechanics for Isurini Sirisena

Question

A boy in a stationary boat on a still pond has lost his oars in the water. In order to get the boat moving again, he throws his rucksack horizontally out of the boat with a speed of 4 m s−1.

Mass of boat = 60 kg; mass of boy = 40 kg; mass of rucksack = 5 kg

(a) How fast will this action make the boat move?

(b) If he throws the rucksack by exerting a force on it for 0.2 s, how much force does he exert?

Answer 1

(a) According to momentum conservation:

$$0=m_rv_r-(M+m)v,\\\space\\ v=\frac{m_rv_r}{M+m}=\frac{5\cdot4}{60+40}=0.2\text{ m/s}.$$

(b) The change in momentum of the rucksack initially at rest is

$$\Delta p=m_rv_r-m_r\cdot0.$$

The force is

$$F=\frac{\Delta p}{t}=\frac{m_rv_r}{t}=100\text{ N}.$$