A 1 kg projectile is initially carried on a 9 kg gun-trolley system. The complete 10 kg system moves with speed 4 m/s on a smooth horizontal track. The projectile is fired forward with speed 20 m/s relative to the trolley. If the speed of the trolley after firing is N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A 1 kg projectile is initially carried on a 9 kg gun-trolley system. The complete 10 kg system moves with speed 4 m/s on a smooth horizontal track. The projectile is fired forward with speed 20 m/s relative to the trolley. If the speed of the trolley after firing is N m/s, find N.

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

G1 Physics · Accepted Answer

Initial momentum of the complete system is p(initial) = 10×4 = 40 kg·m/s. Let the trolley speed after firing be V in the original direction. Since the projectile moves 20 m/s forward relative to the trolley, its ground speed is V+20. Momentum conservation gives 9V + 1(V+20) = 40. Therefore 10V+20 = 40, so V = 2 m/s. Hence N = 2.