A gun of mass 1.98 kg fires a bullet of mass 0.02 kg. Before firing, the gun-bullet system is at rest. The muzzle velocity of the bullet relative to the recoiling gun is 500 m/s. If the recoil speed of the gun is N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A gun of mass 1.98 kg fires a bullet of mass 0.02 kg. Before firing, the gun-bullet system is at rest. The muzzle velocity of the bullet relative to the recoiling gun is 500 m/s. If the recoil speed of the gun is N m/s, find N.

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

G1 Physics · Accepted Answer

Let the gun recoil with speed V to the left. Take right as positive, so gun velocity is −V. Let the bullet speed relative to ground be u. The given muzzle velocity is relative velocity: u − (−V) = u+V = 500, so u = 500−V. Momentum conservation gives 0.02(500−V) + 1.98(−V) = 0. Therefore 10 − 0.02V − 1.98V = 0, so 10 − 2V = 0. Hence V = 5 m/s and N = 5.