Answer to Question #151373 in Classical Mechanics for Isurini Sirisena

Question #151373

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?


1
Expert's answer
2020-12-17T07:27:32-0500

(a) According to momentum conservation:


0=mrvr(M+m)v, v=mrvrM+m=5460+40=0.2 m/s.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


Δp=mrvrmr0.\Delta p=m_rv_r-m_r\cdot0.

The force is


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


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