Five hoboes, each with mass m, stand on a railway flatcar of mass M. They jump o

Question

Five hoboes, each with mass m, stand on a railway flatcar of mass M. They jump off one end of the flatcar with velocity u relative to the car. The car rolls in the opposite direction without friction. What is the final velocity of the flatcar if all the men jump at the same time? Data: m = 69 kg; M = 280 kg; u = 2.9 m/s. Tries 0/25 What is the final velocity of the flatcar if they jump off one at a time? Does case (a) or case (b) yield the largest final velocity of the flat car? Can you give a simple physical explanation for your answer? Tries 0/25

Explanation / Answer

I am assuming you have a calculator and know how to use it. a) if they all jump off at the same time, your conservation of momentum equation will be: 5m*u=Mv. b) if they jump off one at a time, it gets more complicated because each man who jumps is transferring momentum to a progressively less massive object. When the first man jumps, conservation of momentum gives you: m*u=(4m+M)*v1 When the second jumps: m*u=(3m+M)*v2 When the third jumps: m*u=(2m+M)*v3 When the fourth jumps: m*u=(m+M)*v4 When the last jumps: m*u=M*v5 The final velocity of the car is v1+v2+v3+v4+v5.

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