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Question

A man of mass 80 kg jumps from a trolley of mass 20 kg standing on a smooth surface, with an absolute velocity of 3 m/s. The recoiling speed of the trolley is

A
12 m/s
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B
10 m/s
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C
8 m/s
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D
11 m/s
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Solution

The correct option is A 12 m/s
Given:
Mass of man; m1=80 kg
Mass of trolley; m2=20 kg
Final velocity of man; v1=3 m/s
Initial velocity of man (u1) and trolley (u2) are zero as both are at rest. Let (v2) be the final velocity of trolley.

Considering (man+trolley) as system. As there are no net external force in horizontal direction on the system.
Applying principle of conservation of linear momentum (PCLM) in horizontal direction,
m1u1+m2u2=m1v1+m2v2
0=80×3+20×v2
v2=12 m/s
Here negative (- ve) sign shows that trolley moves in the opposite direction of man.
Recoiling speed of trolley=12 m/s

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