A 35 kg boy running at a velocity of 2 m/sec to the right, jumps onto a trolley at rest of mass 70 kg. What is the speed of the trolley and the boy after the boy has jumped in ?

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Solution

Let $v_{1}$ and $v_{2}$ be the velocities of the boy and the trolley before the boy jumps in.

$v_{1} = 2$ and $v_{2} = 0$

The momentum p of the system boy-trolley before the jump,

p = Momentum of Boy + Momentum of trolley

$p = 35 \times 2 + 70 \times 0 = 70 K g m / s e c$

Let $V$ be the velocity of trolley ( with the boy in it ), the momentum of the trolley is

$p = (35 + 70) V$

By conservation of momentum, momenta are equal before and after interaction.

$70 = (35 + 70) V$

$V = 0.7 m / s e c t o t h e r i g h t$

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