A man of mass 60 kg stands at one end of a uniform boat of mass 40 kg and length 5 m. The boat floats on still water and horizontal external force is negligible. The man walks to the other end. If the magnitude of displacement of the boat is N m, find N.
Physics · Center of maas , Momentum and Collision · center of mass and question based on it
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Question

A man of mass 60 kg stands at one end of a uniform boat of mass 40 kg and length 5 m. The boat floats on still water and horizontal external force is negligible. The man walks to the other end. If the magnitude of displacement of the boat is N m, find N.

Physics · Center of maas , Momentum and Collision · center of mass and question based on it

G1 Physics · Accepted Answer

Since there is no horizontal external force, the horizontal position of the centre of mass of the man-plus-boat system remains fixed. Let the boat move a distance x opposite to the man's walking direction. Relative to the water, the man moves 5−x while the boat's centre moves −x. Hence 60(5−x) + 40(−x) = 0. Therefore 300 − 100x = 0, giving x = 3 m. Thus N = 3.