A bullet is fired from the rifle at a speed of 700m s. The rifle, upon recoil, acquires a speed of 1.6m s.

A bullet is fired from the rifle at a speed of 700m s. The rifle, upon recoil, acquires a speed of 1.6m s. Determine the mass of the rifle if the mass of the bullet is 10 g.

Let us write the law of conservation of momentum for a bullet and a rifle, taking into account that the sum of impulses was equal to zero before the shot. Let’s denote the velocity and mass of the rifle through V and M, respectively, the velocity and mass of the bullet through v and m. Since the velocities are directed against each other, their impulses will have different signs:
MV – mv = 0;
M = mv / V = (0.010 kg * 700 m) / 1.6 m = 4.375 kg.
Answer: The mass of the rifle is 4.375 kg.

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