The grenade flew horizontally with an initial speed of 10 m / s and exploded into two fragments of masses m1 = 1 kg

The grenade flew horizontally with an initial speed of 10 m / s and exploded into two fragments of masses m1 = 1 kg and m2 = 1.5 kg. The velocity of the second fragment remained horizontal and increased to v2 = 25m / s. Find the speed and direction of movement of the first fragment.

V = 10 m / s.

m1 = 1 kg.

m2 = 1.5 kg.

V2 “= 25 m / s.

V1 “-?

Since the fragments interact only with each other, they can be considered a closed system. For a closed system, the law of conservation of momentum is valid: m * V = m1 * V1 “+ m2 * V2”.

m1 * V1 “= m * V – m2 * V2”.

V1 “= (m * V – m2 * V2”) / m1.

V1 “= (m * V – m2 * V2”) / m1.

The mass of the grenade m will be the sum of the masses of its fragments m1 and m2: m = m1 + m2.

m = 1 kg + 1.5 kg = 2.5 kg.

V1 “= (2.5 kg * 10 m / s – 1.5 kg * 25 m / s) / 1 kg = – 12.5 m / s.

The “-” sign indicates that the speed of movement of the first fragment after the explosion is directed in the opposite direction of the movement of the grenade.

Answer: the first fragment will move in the opposite direction of the movement of the grenade with a speed V1 “= 12.5 m / s.