Question

A trolley of mass 200 kg moves with a uniform speed of 36 km/h 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 to 4 m/s relative to the trolley in a direction opposite to the trolley's motion and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

• A. 10.4 m/s, 24 m
• B. 10.4 m/s, 22 m
• C. 9.2 m/s, 26 m
• D. 10.4 m/s, 26 m

Answer 1

The correct option is D

10.4 m/s, 26 m

We are given that

Mass of the trolley, M = 200 kg

Speed of the trolley, v = 36 km/h = 10 m/s

Mass of the child, m = 20 kg

Momentum of the system before the child starts running,

$p_1$ = (200 + 20) 10 = 2200 kg m/s

Let v' be the final speed of the trolley when the child on the trolley is running at a speed of 4 m/s relative to the trolley and in a direction opposite to the motion of the trolley.

Clearly, the speed of the child relative to the Earth = (v' - 4)

Momentum of the system when the child is running

$p_2$ = 200 v' + 20 (v' - 4) = 200 v' - 80

Since there is no external force on the system, $p_2$ = $p_1$

or 220 v' - 80 = 2200 or v' = $\frac{2280}{220}=10.4m/s$

Obviously , time taken by the child to run from one end to the other of the trolley, i.e., $t=\frac{10m}{4m/s}=2$

Distance moved by the trolley in $2.5s=velocity\times time=10.4\times 2.5=26m$