A projectile flying horizontally at a speed of 200 m / s breaks into two identical fragments, one of which

A projectile flying horizontally at a speed of 200 m / s breaks into two identical fragments, one of which flies in the opposite direction at a speed of 200 m / s. How fast does the second shard fly?

Vsn = 200 m / s.

m1 = m2 = m / 2.

V1 “= 200 m / s.

V2 “-?

For the projectile, the impulse conservation law is valid: m * Vsn = m1 * V1 “+ m2 * V2”, where m is the mass of the entire projectile, Vsn is the projectile velocity before bursting, m1, m2 are the mass of fragments after the projectile burst, V1 “, V2” is the speed of the fragments after rupture.

Since m1 = m2 = m / 2 and one fragment flew in the opposite direction of the projectile movement, then for projections the law of conservation of momentum will take the form: m * Vсн = – m * V1 “/ 2 + m * V2” / 2.

m * V2 “/ 2 = m * Vсн + m * V1” / 2.

V2 “= 2 * m * Vsn / m + m * V1” / m = 2 * Vsn + V1 “.

V2 “= 2 * 200 m / s + 200 m / s = 600 m / s.

Answer: after the rupture, the second fragment moved at a speed V2 “= 600 m / s in the direction of the projectile movement until the rupture.