---
title: "A person of mass \\(m\\) stands at the left end of a uniform boat of mass \\(M\\), where \\(M > m\\). The boat has length \\(L\\) and floats at rest on calm water where horizontal drag forces are negligible. The person walks to the right end of the boat and stops. Which of the following correctly describes the net displacement of the center of mass of the person-boat system relative to the water, and compares the magnitude of the boat’s displacement \\(|\\Delta x_{\\text{boat}}|\\) to that of the person \\(|\\Delta x_{\\text{person}}|\\) relative to the water?"
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url: "https://nerd-notes.com/ubq/124276/"
date_modified: "2026-09-28T14:04:37+00:00"
---

# A person of mass \(m\) stands at the left end of a uniform boat of mass \(M\), where \(M > m\). The boat has length \(L\) and floats at rest on calm water where horizontal drag forces are negligible. The person walks to the right end of the boat and stops. Which of the following correctly describes the net displacement of the center of mass of the person-boat system relative to the water, and compares the magnitude of the boat’s displacement \(|\Delta x_{\text{boat}}|\) to that of the person \(|\Delta x_{\text{person}}|\) relative to the water?

A person of mass \(m\) stands at the left end of a uniform boat of mass \(M\), where \(M > m\). The boat has length \(L\) and floats at rest on calm water where horizontal drag forces are negligible. The person walks to the right end of the boat and stops. Which of the following correctly describes the net displacement of the center of mass of the person-boat system relative to the water, and compares the magnitude of the boat's displacement \(|\Delta x_{\text{boat}}|\) to that of the person \(|\Delta x_{\text{person}}|\) relative to the water?

![A horizontal dashed line represents the water surface. Floating at the surface is a symmetric boat hull drawn as a wide flat-bottomed polygon with slightly angled ends, labeled with mass \(M\) in its center. The total horizontal length between the left and right ends of the boat is indicated by a horizontal double-headed dimension arrow below the hull labeled \(L\). At the far left flat deck of the boat stands a vertical simplified figure representing a person, labeled with mass \(m\) directly above its head. A single horizontal arrow above the person points to the right toward the opposite end of the boat. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604277-03bywG.jpg)

- **A.** Center-of-mass displacement: Directed to the right; Comparison of magnitudes: \(|\Delta x_{\text{boat}}| > |\Delta x_{\text{person}}|\)
- **B.** Center-of-mass displacement: Directed to the right; Comparison of magnitudes: \(|\Delta x_{\text{boat}}| < |\Delta x_{\text{person}}|\)
- **C.** Center-of-mass displacement: Zero; Comparison of magnitudes: \(|\Delta x_{\text{boat}}| < |\Delta x_{\text{person}}|\)
- **D.** Center-of-mass displacement: Zero; Comparison of magnitudes: \(|\Delta x_{\text{boat}}| > |\Delta x_{\text{person}}|\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124276/*