Question

A boy of mass 40 kg running at 5 m/s jumps on a cart of 20 kg moving in the same direction at 2 m/s. Find their common velocity.

Answer 1

The momentum of the system, consisting of the boy and the cart, must be conserved in the absence of the net external force.

Initial momentum of the system,
$p_i$ = $m_1$$u_1$ + $m_2$$u_2$
$p_i$ = 40 x 5 + 20 x 2 = 240 kg m/s

Finally, both the boy and the cart are moving together with the same velocity.
Hence, the final momentum of the system, $p_f$ = (40 + 20) x v = 60v

By the conservation of momentum,
$p_i$ = $p_f$
⇒ 240 = 60v
⇒ v = $\frac{240}{60}$
v = 4 m/s