A 4-kg rifle firing an 8-g bullet at 650 m/s obeys the law of conservation of momentum. Determine the recoil speed of the rifle.
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The law of conservation of momentum states that the total momentum before an event must be equal to the total momentum after the event. In this case, the event is the firing of the bullet.
Before the bullet is fired, the total momentum is 0 (because neither the rifle nor the bullet is moving). After the bullet is fired, the bullet has a momentum of (mass of bullet) * (velocity of bullet) = (0.008 kg) * (650 m/s) = 5.2 kg*m/s.
Because the total momentum must remain 0, the rifle must have a momentum of -5.2 kg*m/s (negative because it's moving in the opposite direction of the bullet).
The recoil speed of the rifle is then (momentum of rifle) / (mass of rifle) = (-5.2 kg*m/s) / (4 kg) = -1.3 m/s.
The negative sign indicates that the rifle is moving in the opposite direction of the bullet, but in terms of speed, we can say that the recoil speed of the rifle is 1.3 m/s.
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