A trolly of mass 200kg moves with a uniform speed of 36 kmh 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 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 ?

On a frictionless track, there’s no external horizontal force on the trolley child system, so total linear momentum is conserved.

Initial speed v=36 km/h=10 m/s.

Let the trolley’s speed (w.r.t. ground) while the child runs be v′. The child runs opposite the trolley at 4 m/s relative to the trolley, so the child’s ground speed is v′−4.

Conservation of momentum: 200+2010=200v′+20v′−4v′10.36 m/s.

Time to cross 10 m at 4 m/s relative speed is 2.5 s, so trolley displacement 10.362.5 = 25.9 m.