A projectile is launched from the ground and follows a parabolic trajectory. At the peak of its motion, internal explosive forces cause the projectile to break into two fragments of unequal mass that move in different directions. Air resistance is negligible. Which of the following claims correctly describes the motion of the center of mass of the two-fragment system after the explosion?

Consider the following statements about the system's motion after the explosion:
I. The acceleration of the center of mass remains equal to the acceleration due to gravity.
II. The horizontal component of the velocity of the center of mass remains constant.
III. The path of the center of mass is a straight line.