Q. 283.8( 18 Votes )

A trolley of mass

Answer :


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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