# A bullet takes off from the rifle at a speed of 700 m / s. the rifle, upon recoil, acquires a speed of 1.6 m / s.

A bullet takes off from the rifle at a speed of 700 m / s. the rifle, upon recoil, acquires a speed of 1.6 m / s. Determine the mass of the rifle if the mass of the bullet is 10 grams.

Vp = 700 m / s. Vw = 1.6 m / s. mp = 10 g = 0.01 kg.
mv -?
Let’s use the law of conservation of momentum: in a closed system of bodies, the total momentum of the system remains unchanged. The momentum of the body P is the product of the body’s mass m by its velocity V: P = m * V. Before the shot, the impulse of the system is equal to 0. The impulse of the bullet after the shot: Pp = mp * Vp. Rifle impulse after firing: Рв = – mв * Vв. The “-” sign means that the speed of the rifle is directed in the opposite direction. mp * Vp – mw * Vw = 0.mp * Vp = mw * Vw. mv = mp * Vp / Vv. mw = 0.01 kg * 700 m / s / 1.6 m / s = 4.375 kg.
Answer: the mass of the rifle is mw = 4.375 kg.

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