Question

A shopping trolley, weighing 10 kg was sliding on a horizontal,
frictionless surface with a velocity of 3 m/s. If bags weighing 1kg
was being added to it on regular occasions, then find the velocity
of the trolley after 5 bags
had been added.
(A) 2 m/s
(B) 1 m/s
(C) 3 m/s
(D) 0 m/s

Answer 1

Explanation:

Mass of the trolley, M=200kg

Speed of the trolley, v=36km/h=10m/s

Mass of the boy, m=20kg

Initial momentum of the system of the boy and the trolley

     =(M+m)v 

     =(200+20)×10

     =2200kg m/s

Let v′ be the final velocity of the trolley with respect to the ground.

Final velocity of the boy with respect to the ground  =v′−4

Final momentum =Mv′+m(v′−4)

                             =200v′+20v′−80

From the conservation of linear momentum:

Initial momentum= Final momentum

                  2200=220v′−80

                    ∴ v′=2280/220=10.36m/s

Length of the trolley, l=10m

Speed of the boy, v′′=4m/s 

Time taken by the boy to run, t=10/4=2.5s

∴ Distance moved by the trolley =v′′×t= 10.36×2.5=25.9m