When a body explodes into two different masses, the conservation of momentum principle applies, allowing for the calculation of their velocities post-explosion. The initial momentum must equal the total momentum after the explosion, which can be expressed with the equation involving the masses and their respective velocities. The discussion highlights that while the two masses may not have the same kinetic energy, they must move in such a way that the total momentum remains zero, typically requiring them to move in opposite directions. However, if they move at different angles, the analysis must account for the vector nature of momentum. Ultimately, the conversation emphasizes the need for precise definitions and understanding of kinetic energy and momentum in relation to the explosion.