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 of 4 m s⁻¹ relative to the trolley in a direction opposite to its 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?

Answer 1

Hey mate,

◆ Answer-
v = 10.3 m/s
D = 25.75 m

◆ Given-
M = 200 kg
m = 20 kg
u = 36 km/h = 10 m/s
d = 10 m
v-v' = 4 m/s

◆ Solution-
Initial Momentum is given by
P1 = (M+m)u       
P1 = (200+20)10
P1 = 2200 kgm/s

Now Final Momentum is
P2 = Mv + mv'
P2 = 200v + 20(v-4)
P2 = 220v-80

Using law of conservation of momentum-
Initial Momentum = Final Momentum
P1 = P2
2200 = 200v-80
v = 10.3 m/s

So final velocity of trolley = 10.3 m/s.

Time taken by boy to fall-
t = distance from edge / relative speed
t = 10/4
t = 2.5 s

Distance covered by trolley -
D = 10.3×2.5
D = 25.75 m 

Hope this helped you...