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Question

A cart of mass M=100 kg is at rest over a smooth horizontal surface. A boy of mass m=50 kg is standing over the cart. If he jumps from the cart with a horizontal velocity of 20 ms1, the final velocity of the cart is :

A
10 ms1
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B
20 ms1
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C
10 ms1
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D
20 ms1
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Solution

The correct option is C 10 ms1
Given:
Mass of boy (m1) = 50 kg
Mass of cart (m2) = 100 kg
Initial velocity of boy (u1) = 0 ms1
Initial velocity of cart (u2) = 0 ms1
Final velocity of boy (v1) = 20 ms1
Final velocity of cart (v2) = ?
According to the law of conservation of momentum,
Initial momentum of the system = Final momentum of the system
m1u1+m2u2=m1v1+m2v2
0 + 0 =50×20+100×v2
v2=10 ms1

Negative sign indicates the velocity of cart is in opposite direction of the velocity of the boy.

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