A grenade flying at a speed of v = 5m / s exploded into two fragments. The mass m1 of the first fragment is 1.5 times greater

A grenade flying at a speed of v = 5m / s exploded into two fragments. The mass m1 of the first fragment is 1.5 times greater than the mass m2 of the second fragment (m1 = 1.5 m2). The first fragment continued to move in the same direction at a speed of v1 = 15 m / s. Find the velocity v2 of the smaller fragment.

The x axis along the velocity vector of the grenade v0:
Impulse of fragments before explosion:
p1 = v0 (m1 + m2).
Impulse of fragments after explosion:
p2 = v1m1 + v2m2, where v1 and v2 are the velocities of the first and second fragments. The direction of v2 is still unknown. Suppose it coincides with v0.
The impulses before and after the explosion are equal:
p1 = p2;
v0 (m1 + m2) = v1m1 + v2m2;
Replacement m1 = 1.5m2
v0 (1.5m2 + m2) = v1 * 1.5m2 + v2m2
2.5 v0m2 = v1m2 + v2m2;
2.5v0 = 1.5v1 + v2;
v2 = 2.5v0 – 1.5v1 = 2.5 * 5 m / s – 1.5 * 15 m / s = -10 m / s.
Answer: -10 m / s (sign “-” – the speed of the fragment is directed against the x axis).