The isolated particle of mass m is moving horizontally along the x-axis and suddenly explodes into two fragments. The center of mass, according to the principle of conservation of momentum, remains unchanged if no external forces act on the system. The particle breaks into two fragments, one with a mass of m/4 and the other with a mass of 3m/4.

Given after the explosion that the smaller fragment is located at y = +15 cm, use the idea that the overall center of mass for the system must remain at the same vertical position as before the explosion, which was at y = 0.

The position of the center of mass is determined by the masses and their respective positions. Since the smaller fragment is at y = +15 cm, the position of the larger fragment must be such that it balances this position according to their mass ratio. By conservation, we determine that the larger fragment must be positioned at y = -5 cm. This negative position denotes that it lies below the initial center of mass level, making sure the global system maintains the center of mass position after detonation.

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