A stationary boat of mass 100 kg carries two persons of masses 20 kg and 30 kg. Simultaneously, the 20 kg person jumps to the right with speed 5 m/s relative to the boat, while the 30 kg person jumps to the left with speed 3 m/s relative to the boat. If the magnitude of the boat's velocity is 1/N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A stationary boat of mass 100 kg carries two persons of masses 20 kg and 30 kg. Simultaneously, the 20 kg person jumps to the right with speed 5 m/s relative to the boat, while the 30 kg person jumps to the left with speed 3 m/s relative to the boat. If the magnitude of the boat's velocity is 1/N m/s, find N.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

G1 Physics · Accepted Answer

Let the boat velocity be V, positive to the right. The 20 kg person's ground velocity is V+5. The 30 kg person's ground velocity is V−3. Initial momentum is zero, so 100V + 20(V+5) + 30(V−3) = 0. Thus 100V+20V+100+30V−90 = 0, giving 150V+10 = 0. Therefore V = −1/15 m/s. The boat moves left with speed 1/15 m/s, so N = 15.