---
title: "A stationary object of total mass \\(M\\) on a frictionless horizontal surface explodes into three fragments. Two of the fragments, each of mass \\(m\\), move away along the surface with equal speed \\(v_0\\) such that the angle between their velocity vectors is \\(\\theta\\), where \\(0 < \\theta < \\pi\\). The third fragment has the remaining mass of the object. Which of the following is a correct expression for the speed of the third fragment immediately after the explosion?"
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url: "https://nerd-notes.com/ubq/124346/"
date_modified: "2026-09-28T14:04:55+00:00"
---

# A stationary object of total mass \(M\) on a frictionless horizontal surface explodes into three fragments. Two of the fragments, each of mass \(m\), move away along the surface with equal speed \(v_0\) such that the angle between their velocity vectors is \(\theta\), where \(0 < \theta < \pi\). The third fragment has the remaining mass of the object. Which of the following is a correct expression for the speed of the third fragment immediately after the explosion?

A stationary object of total mass \(M\) on a frictionless horizontal surface explodes into three fragments. Two of the fragments, each of mass \(m\), move away along the surface with equal speed \(v_0\) such that the angle between their velocity vectors is \(\theta\), where \(0 < \theta < \pi\). The third fragment has the remaining mass of the object. Which of the following is a correct expression for the speed of the third fragment immediately after the explosion?

![A top-down schematic view showing two fragments moving away from a detonation point on a horizontal plane. A small open circle marks the initial detonation location. From the open circle, exactly two solid arrows of equal length extend outward into the right half-plane: one arrow points toward the upper right and terminates at a solid circular disk labeled m, with the arrow labeled v_0; the second arrow points toward the lower right and terminates at an identical solid circular disk labeled m, with the arrow labeled v_0. A curved double-ended arc spans between the two arrows and is labeled \theta. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604295-oYNSPW.jpg)

- **A.** \(\dfrac{2m v_0}{M} \cos\left(\dfrac{\theta}{2}\right)\)
- **B.** \(\dfrac{2m v_0}{M - 2m} \cos\left(\dfrac{\theta}{2}\right)\)
- **C.** \(\dfrac{2m v_0}{M - 2m} \cos\theta\)
- **D.** \(\dfrac{2m v_0}{M - 2m} \sin\left(\dfrac{\theta}{2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124346/*