Man-Boat System Kinetic Energy Increase · PhysicsBowl 2021 #38

Physics · mechanics

Problem

A man of mass m, gets off a boat by leaping to the left in an exactly horizontal direction. Both the man and the boat were initially stationary. Immediately after the leap, the boat of mass M, is observed to be moving to the right at speed v. What is the increase of the kinetic energy in the man-boat system? (Neglect the resistive force of the water) A) 12Mv2\frac{1}{2}Mv^2 B) 12mv2\frac{1}{2}mv^2 C) 12(M+m)v2\frac{1}{2}(M+m)v^2 D) 12(M+M2m)v2\frac{1}{2}\left(M+\frac{M^2}{m}\right)v^2 E) 12Mm(M+m)v2\frac{1}{2}\frac{Mm}{(M+m)}v^2

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