Question

A girl of mass 50kg jumps out of a moving boat of mass 300kg on the bank with a horizontal velocity of 3 m/s.with what velocity will the boat begin to move backwards

Answer 1

Take the girl and the boat as a single system. Since there is no external force acting on the system, the net momentum is conserved. That is, the center of the mass of the system will be stationary.

(M*X+m*x)/(M+m) = 0, as center of mass is stationary, where M is mass of girl, and m is mass of cart.
Differentiating that equation with respect to time, you will get (M*V+m*v)/(M+m) = 0, where V and v are velocities of girl and boat respectively. So, M*V=-m*v.
Substituting values, 50*3=-300*v
So, v=-0.5m/s. So, it moves backwards with velocity 1/2m/s.

Answer 2

300/50=6
6/3=2
answer is 2
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