A grenade flying at a speed of 15m / s exploded into two parts with weights of 6kg and 14kg. The speed of the larger

A grenade flying at a speed of 15m / s exploded into two parts with weights of 6kg and 14kg. The speed of the larger shrapnel is 24m / s directed the same as the speed of the grenade before the explosion. Find the direction and speed modulus of the smaller fragment.

m1 = 6 kg.

m2 = 14 kg.

V = 15 m / s.

V2 = 24 m / s.

V1 -?

When a grenade ruptures, it can be considered a closed system, for which the law of conservation of momentum is valid: the sum of the impulses of a closed system does not change.

(m1 + m2) * V = m1 * V1 + m2 * V2, where (m1 + m2) * V is the impulse of the grenade before bursting, m1 * V1 is the impulse of the smaller fragment, m2 * V2 is the impulse of the larger fragment.

m1 * V1 = (m1 + m2) * V – m2 * V2.

V1 = ((m1 + m2) * V – m2 * V2) / m1.

V1 = ((6 kg + 14 kg) * 15 m / s – 14 kg * 24 m / s) / 6 kg = – 6 m / s.

The “-” sign indicates that the smaller shard will move in the opposite direction to the movement of the grenade and the larger shard.

Answer: a smaller fragment will move in the opposite direction of the movement of the grenade at a speed of V1 = 6 m / s.