A man and trolley together have mass 90 kg. A 10 kg package is initially on the trolley, and the complete system is at rest on a smooth horizontal surface. The package is thrown horizontally with speed 6 m/s relative to the trolley. If the recoil speed of the man-trolley system is N/10 m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A man and trolley together have mass 90 kg. A 10 kg package is initially on the trolley, and the complete system is at rest on a smooth horizontal surface. The package is thrown horizontally with speed 6 m/s relative to the trolley. If the recoil speed of the man-trolley system is N/10 m/s, find N.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

G1 Physics · Accepted Answer

Let the man-trolley system recoil with speed V opposite to the thrown package. Take the package direction as positive. Then trolley velocity is −V. If the package is thrown at 6 m/s relative to the trolley, its ground speed is 6−V. Since initial momentum is zero, 10(6−V) + 90(−V) = 0. Thus 60 − 10V − 90V = 0, so 100V = 60 and V = 0.6 m/s = 6/10 m/s. Hence N = 6.