Question

A trolley of mass 200 kg moves with a uniform speed of $36kmh^{- 1}$on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed $4ms^{- 1}$relative to the trolley in a direction opposite to its motion, and jumps out of the trolley. The final speed of the trolley is:

• A. $8.4ms^{- 1}$
• B. $10.4ms^{- 1}$
• C. $12.2ms^{- 1}$
• D. $14.6ms^{- 1}$

Answer 1

Answer: (B)

$10.4ms^{- 1}$

Answer 2

Here,

Mass of the trolley, M = 200 Kg

Mass of the child, m = 20 kg

Speed of the trolley, V = 36 km h^-1

=$36 \times \frac{5}{18}ms^{- 1} = 10ms^{- 1}$

Before the child starts running, momentum of the system

$p_{i} = (m + M)v = (20Kg + 200kg) \times 10ms^{- 1}$

$= 2200kgms^{- 1}$

Let $v'$is the final speed of the trolley.

When the child starts running with a speed of $4ms^{- 1}$in a direction opposite to the trolley,

$\therefore$speed of the child relative to ground =$v' - 4$

Momentum of the system when child is running

$p_{f} = 200v' + 20(v' - 4) = 220v' - 80$

According to law of conservation of momentum,

$p_{i} = p_{f}$

$2200 = 220v' - 80$

$220v' = 2280$

$v' = \frac{2280}{220} = 10.4ms^{- 1}$