Question

A (trolley+child of total mass $200kg$ is moving with a uniform speed of $35km/h$ on a frictionless track. The child of mass $20kg$ starts running on the trolley from one end to the other ($10m$ away) with a speed of $10m{s}^{-1}$ relative to the trolley in the direction of the trolley's motion and jumps out of the trolley with the same relative velocity. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

Answer 1

By momentum conservation.

$\Rightarrow 200\times \frac{3.5}{3.6}m/s=180v+20(4+v)$

$200\times \frac{3.5}{3.6}=200v+20\times 10$

$200v=200(\frac{35}{3.6}-1)$

$\Rightarrow v=8.722m/s$

$\Rightarrow$ Time taken by boy to travel $10m.$ is $t=\frac{10}{10}=1se.$

In $1sec$ trolley moves distance $D=vt$

$=8.722m.$

Hence, the answer is $8.722m.$