A man of mass 20 kg stands on a stationary boat of mass 80 kg. He jumps horizontally with speed 5 m/s relative to the boat. Neglect horizontal external forces. If the recoil speed of the boat is N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A man of mass 20 kg stands on a stationary boat of mass 80 kg. He jumps horizontally with speed 5 m/s relative to the boat. Neglect horizontal external forces. If the recoil speed of the boat is N m/s, find N.

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

G1 Physics · Accepted Answer

Let the boat recoil with speed V opposite to the man's jump. Take the man's jump direction as positive, so boat velocity is −V. The man's speed relative to ground is 5−V because his speed relative to the boat is 5 m/s. Momentum conservation gives 20(5−V) + 80(−V) = 0. Hence 100 − 20V − 80V = 0, so V = 1 m/s. Therefore N = 1.