A projectile of mass \(M\) is launched over level ground and travels along a parabolic path in the absence of air resistance. At the apex of its trajectory, an internal explosive charge detonates, breaking the projectile into two fragments of masses \(m_1\) and \(m_2\), where \(m_1 > m_2\). While both fragments are still in flight, which of the following correctly describes the motion of the center of mass of the two-fragment system and provides the correct justification?