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Question

A boy of mass 50 kg mass runs and jumps onto a stationary cart of mass 80 kg. After landing, he moves along with the cart at a speed of 0.4 ms1. What is the initial velocity of the boy?

A
150 kgm/s
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B
20 kgm/s
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C
50 kgm/s
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D
100 kgm/s
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Solution

The correct option is D 100 kgm/s

Given,mass of the boy,m1=50 kg
Mass of cart,m2=80 kg
Initial velocity of cart, u2=0
Final velocity of cart = Final velocity of boy, v=0.8 ms1
Let initial velocity of boy be u1.
Initial momentum of boy =m1u1=50u1
Initial momentum of cart =0 (initially at rest)
Final momentum of boy =m1v=50×0.8=40 kgms1
Final momentum of cart =m2v=80×0.8=64 kgms1

By law of conservation of momentum:
Total initial momentum = Total final momentum
m1u1+0=m1v+m2vu1=(m1+m2)v50=130×0.850u1=2.08 ms1
Therefore, the initial velocity of the boy is 2.08 ms1


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