A 45.0-kg girl stands on a 13.0-kg wagon holding two 18.0-kg weights. She throws the weights horizontally off the back of the wagon at a speed of 6.5 m/s relative to herself . Assuming that the wagon was at rest initially, what is the speed of the girl relative to the ground after she throws both weights at the same time

v = 4.0 m/s

Explanation:

Assuming no external forces acting during the instant that the girl throws the weights, total momentum must be conserved.Since all the masses at rest initially, the initial momentum must be zero.So, due to momentum must keep constant, final momentum must be zero too, as follows:

       

Assuming the direction towards the back of the wagon as positive, and replacing the masses in (1), we can solve for vg, as follows:

       

This means that the girl (along with the wagon on she is standing) will move at a speed of 4.0 m/s in an opposite direction to the one she threw the weights.

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