Question

A boy of mass 50 kg running at 5 m/s jumps onto a 20 kg trolley traveling in the same direction at 1.5 m/s. What is their common velocity?

Answer 1

When we consider both body and trolley to be our system, the net external force acting on the system is zero. So, we can conserve momentum of the system.
Let the boy and trolley move with common velocity v.
Momentum of the system just before the jump = Momentum of the system just after the jump
$\Rightarrow 50\times 5+20\times 1.5=(50+20)\times v$
$\Rightarrow 250+30=70v$
$\Rightarrow 280=70v$
$\Rightarrow v=4m/s$
So, the common velocity is 4 m/s.