The hunter fires a shot from a stationary boat. What speed does the boat acquire at the time of the shot

The hunter fires a shot from a stationary boat. What speed does the boat acquire at the time of the shot, if the mass of the boat with the hunter is 100 kg, the initial velocity of the shot is 350 m / s, and its mass is 30 g. The barrel of the gun at the time of the shot is parallel to the surface of the water. Neglect water resistance.

ml = 100 kg.

Vd “= 350 m / s.

md = 30 g = 0.03 kg.

Vl “-?

For a closed-loop system, the momentum conservation law is valid: the sum of the impulses of a closed-loop system does not change.

(ml + md) * V = ml * Vl “+ md * Vd”.

Since before the shot the hunter was stationary V = 0 m / s, then the law of conservation of momentum will take the form: ml * Vl “+ md * Vd” = 0.

ml * Vl “= – md * Vd”.

Vl “= – md * Vd / ml.

The “-” sign indicates that the boat with the hunter after the shot will move in the opposite direction of the shot.

Vl “= 0.03 kg * 350 m / s / 100 kg = 0.105 m / s.

Answer: after the shot, the hunter with the boat will move in the opposite direction with a speed Vl “= 0.105 m / s.