---
title: "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?"
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url: "https://nerd-notes.com/ubq/120552/"
date_modified: "2026-08-23T04:41:33+00:00"
---

# 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?

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?

![A 2D coordinate diagram showing a horizontal ground line. A solid curved parabolic trajectory starts from the ground on the left at the origin and rises to a peak labeled Apex. At the peak, the path splits into two diverging dashed paths representing two fragments, one path flying forward and upward and the other path flying forward and downward. A third dashed-dotted curve continues along the original parabolic arc from the apex down to the ground on the right. An acceleration arrow points vertically downward labeled \(\vec{g}\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460093-VoUQ3p.jpg)

- **A.** The trajectory of the center of mass shifts toward the path of the heavier fragment \(m_1\) because the internal explosive force imparts a greater net momentum to the piece with larger mass.
- **B.** The trajectory of the center of mass continues along the original parabolic path because mechanical energy is conserved during the explosion, keeping the total kinetic energy of the center of mass constant.
- **C.** The trajectory of the center of mass continues along the original parabolic path because the explosive forces are purely internal to the system, so the net external force remains \(\sum \vec{F}_{\text{ext}} = M\vec{g}\) and \(\vec{a}_{\text{cm}} = \vec{g}\).
- **D.** The trajectory of the center of mass deflects downward more steeply because the sudden release of chemical potential energy increases the downward acceleration of the center of mass.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120552/*