A grenade weighing 1 kg, flying at a speed of 20 m / s to the west, is torn into two fragments.

A grenade weighing 1 kg, flying at a speed of 20 m / s to the west, is torn into two fragments. One with a mass of 0.2 kg begins to move at a speed of 500 m / s in the direction of the grenade’s flight. How fast will the other shard fly?

m = 1 kg.

V = 20 m / s.

m1 = 0.2 kg.

V1 “= 500 m / s.

V2 “-?

Let us write the law of conservation of momentum in vector form: m * V = m1 * V1 “+ m2 * V2”, where m * V is the impulse of the projectile before the explosion, m1 * V1 “is the impulse of the first fragment after the explosion, m2 * V2” is the impulse of the second fragment after the explosion.

Let us express the mass of the second fragment m2: m2 = m – m1.

m * V = m1 * V1 “+ (m – m1) * V2”.

V2 “= (m * V – m1 * V1”) / (m – m1).

V2 “= (1 kg * 20 m / s – 0.2 kg * 500 m / s) / (1 kg – 0.2 kg) = – 100 m / s.

The “-” sign indicates that the speed of the second fragment, directed in the opposite direction of the movement of the projectile, until the rupture.

Answer: after the rupture, the second fragment will move in the opposite direction of the movement of the projectile with a speed of V2 “= 100 m / s.