Question 265: Centre of Mass and Rotational Motion

Question

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms$$-$$1. The velocity of the running man was ___________ ms$$-$$1, when he jumps into the car.

Accepted Answer

Total momentum of (man + trolley) system is always conserved
Initially man was moving with velocity v
1
and trolley was at rest, finally both were moving with velocity 2 ms
$$-$$1
after man jumps on the trolley.
So,
$
 \Rightarrow \quad m_{1} v_{1}+0=\left(m_{1}+m_{2}ight) v_{2} $
$
 	ext { Here, } m_{1}=	ext { mass of man }=60 \mathrm{~kg} $
$
 m_{2}=	ext { mass of trolley }=120 \mathrm{~kg} $
$
 v_{1}=	ext { speed of } 	ext { man } $
$
 v_{2}=	ext { speed of man and trolley }=2 \mathrm{~m} / \mathrm{s} $
$
 \Rightarrow 60 	imes v_{1}=(60+120) 	imes 2 $
$
 \Rightarrow v_{1}=\frac{(60+120) 	imes 2}{60}=6 \mathrm{~m} / \mathrm{s}
$

Centre of Mass and Rotational Motion

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms$-1. The velocity of the running man was ___________ ms-$1, when he jumps into the car.

Choose the correct answer: