A projectile of total mass \(M\) is launched from horizontal ground and follows a parabolic trajectory under the influence of uniform downward gravity with negligible air resistance.

At the apex of its trajectory, an internal explosive charge detonates, splitting the projectile into two fragments of unequal masses \(m_1\) and \(m_2\) (where \(m_1 > m_2\)) that fly apart in the vertical plane of motion.

Which of the following statements and justifications correctly describes the motion of the center of mass of the two-fragment system after the explosion while both fragments are in free flight?