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

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 10g.

Vp “= 700 m / s.

Vw “= 1.6 m / s.

mp = 10 g = 0.01 kg.

mv -?

Let us use the law of conservation of momentum for the closed-loop bullet-rifle system: pn + pw = pn “+ pw”, where pn, pn “are the impulse of the bullet before and after the shot, pw, pw” are the impulse of the rifle before and after the shot.

The momentum of a body p is the product of the body’s velocity V and its mass m: p = m * V.

Since the bullet and the rifle are at rest before the shot, their velocities and, accordingly, impulses are equal to 0.

pn “+ pv” = 0.

mp * Vp “+ mw * Vw” = 0.

mp * Vp “= – mw * Vw”.

The sign “-” means that the speed of the bullet and rifle, after firing, are directed in opposite directions.

mv = mp * Vp “/ Vv”.

mw = 0.01 kg * 700 m / s / 1.6 m / s = 4.375 kg.

Answer: the rifle has a mass of mw = 4.375 kg.

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