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Question

A boy of mass 50 kg running at 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s. What is their common velocity?

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Solution

Here the momentum of the system will remain conserved as no external forces are involved.

Total momentum before the boy jumps on the trolley = MBoyuBoy+MTrolley uTrolley = 50 kg × 5 m/s + 20 kg × 1.5 m/s=280 kg m/s

Let the common velocity of the boy and the trolley is 'vCommon'.

Total momentum after the boy jumps on the trolley = MBoy+MTrolley vCommon = 50 kg + 20 kg × vCommon=70 kg × vCommon

Accordding to momentum conservation, Initial momentum = Final momentum

280 kg m/s=70 kg× vCommon vCommon=280 kg m/s70 kg=4 m/s vCommon=4 m/s

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