---
title: "A rocket travels horizontally in deep space where external forces are negligible. At a particular instant, the rocket has total mass \\(M\\) and moves forward with speed \\(v\\) relative to an inertial reference frame. The rocket’s engine expels exhaust gas backward at a constant speed \\(u_{\\text{ex}}\\) relative to the rocket at a constant mass rate \\(R = -\\dfrac{dM}{dt}\\). Which of the following expressions represents the instantaneous rate of change of the rocket’s linear momentum, \\(\\dfrac{d(Mv)}{dt}\\), in the forward direction?"
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url: "https://nerd-notes.com/ubq/120697/"
date_modified: "2026-08-23T04:42:44+00:00"
---

# A rocket travels horizontally in deep space where external forces are negligible. At a particular instant, the rocket has total mass \(M\) and moves forward with speed \(v\) relative to an inertial reference frame. The rocket’s engine expels exhaust gas backward at a constant speed \(u_{\text{ex}}\) relative to the rocket at a constant mass rate \(R = -\dfrac{dM}{dt}\). Which of the following expressions represents the instantaneous rate of change of the rocket’s linear momentum, \(\dfrac{d(Mv)}{dt}\), in the forward direction?

A rocket travels horizontally in deep space where external forces are negligible. At a particular instant, the rocket has total mass \(M\) and moves forward with speed \(v\) relative to an inertial reference frame. The rocket's engine expels exhaust gas backward at a constant speed \(u_{\text{ex}}\) relative to the rocket at a constant mass rate \(R = -\dfrac{dM}{dt}\). Which of the following expressions represents the instantaneous rate of change of the rocket's linear momentum, \(\dfrac{d(Mv)}{dt}\), in the forward direction?

- **A.** \(0\)
- **B.** \(R(u_{\text{ex}} - v)\)
- **C.** \(R u_{\text{ex}}\)
- **D.** \(R(u_{\text{ex}} + v)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120697/*