A $35\ kg$ boy jumps (from rest) into a moving trolley of mass $70\ kg$ and already moving at a velocity of $5\ m/s$ to the right. What is the speed of the trolley after the boy has jumped in?

Given: Mass of the boy $m_{boy}=35\ kg$

Mass of the trolly $m_{trolly}=70\ kg$

Initial velocity of the boy $=0$    [As the boy jumps from the rest]

Initial velocity of the trolly $u=5\ m/s$

Let $v$ be the velocity of the trolly after the boy has jumped in.

To do: We have to find the velocity of the trolly after the boy has jumped in.

Solution:

According to the law of conservation of Momentum:

Total momentum of the boy and trolly before jump $=$ Total momentum of the boy and trolly after the boy jump in

Or $m_{boy}\times0+m_{trolly}\times5=(m_{boy}+m_{trolly})v$

Or $35\times0+70\times5=(35+70)v$

Or $0+350=105v$

Or $v=\frac{350}{105}$

Or $v=3.3\ m/s$

Therefore, the speed of the trolley after the boy has jumped in is $3.3\ m/s$.

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Updated on: 10-Oct-2022

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