Q. 283.8( 18 Votes )

A trolley of mass

Answer :

Given,

Mass of the trolley, m = 200 kg


Speed of the trolley, v=36km/h=(36×1000 m)/(60×60 s)= 10m/s


Mass of the child, m’ = 20 kg


Initial momentum of the system involving the child and the trolley, pi = (m+m’)v


pi = (200 kg + 20 kg)×10 ms-1


pi = 2200 kg m s-1


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


Final velocity of the child with respect to ground, v’’ = Final velocity of trolley with respect to ground – final velocity of child with respect to trolley.


So, v’’ = v’ – 4


Final momentum of the system, pf = mv’ + m’v’’


pf = mv’ + m’(v’-4)


pf = 200v’ + 20(v’-4)


pf = 220v’-80


According to the law of conservation of linear momentum,


Initial momentum (pi) of system = Final momentum (pf) of system


2200 = 220v’-80


220v’ = 2280


v’ = 2280/220


v’ = 10.36 m/s


Length of the trolley, l = 10 m


Speed of the child with respect to trolley, v’ = 4m/s


Time taken by the boy to cover the distance, t = l/v’


t = 10m/4 ms-1


t = 2.5 s


Distance moved by the trolley in this time, s = v’t


s = 10.36 ms-1 × 2.5 s


s = 25.9 m


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