A trolly of mass 200kg moves with a uniform speed of 36 km`//`h on a frictionless track. A child of mass 20kg runs on the trolly from one end to the other (10m away) with a speed of `4m//s` relative to the trolly in a direction opposite to the trolly's motion and jumps out of the trolly. How much has teh trolly moved from the time the child begins to run ?

Explanation

Let there be an observer travelling parallel to the trolley with the same speed. He will observed the initial momentum of the trolley of mass M and child of mass m as zero. When the child jumps in opposite direction, he will observe the increase in the velocity of the trolley by `Deltav`. Let u be the velocity of the child. He will observe child landing at velocity (`u-Deltau)` Therefore, initial momentum = 0
final momentum = `MDeltav-m(u-Deltav)`
Hence, `MDeltav-m(u-Deltav)=0`
When `Deltav=mu//M+m`
Putting values `Deltav=4 xx 20//20+220=ms^(-1)`
The child take 2.5 s to run on the trolley.
Therefore, the trolley moves a distance = `2.5 xx 10.36m= 25.9m`