---
title: "A person of mass \\(m\\) stands at the left end of a uniform flatboat of mass \\(M_1 = 7m\\) and length \\(L\\) that is initially at rest on a frictionless lake. The person walks to the right end of the boat, causing the boat to shift to the left by a distance \\(d_1\\) relative to the water. In a second scenario, the same person stands at the left end of a flatboat of mass \\(M_2 = 3m\\) and length \\(L\\), also initially at rest on the water, and walks to the right end, causing the boat to shift to the left by a distance \\(d_2\\) relative to the water. What is the ratio \\(\\dfrac{d_2}{d_1}\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124325/"
date_modified: "2026-09-28T14:04:49+00:00"
---

# A person of mass \(m\) stands at the left end of a uniform flatboat of mass \(M_1 = 7m\) and length \(L\) that is initially at rest on a frictionless lake. The person walks to the right end of the boat, causing the boat to shift to the left by a distance \(d_1\) relative to the water. In a second scenario, the same person stands at the left end of a flatboat of mass \(M_2 = 3m\) and length \(L\), also initially at rest on the water, and walks to the right end, causing the boat to shift to the left by a distance \(d_2\) relative to the water. What is the ratio \(\dfrac{d_2}{d_1}\)?

A person of mass \(m\) stands at the left end of a uniform flatboat of mass \(M_1 = 7m\) and length \(L\) that is initially at rest on a frictionless lake. The person walks to the right end of the boat, causing the boat to shift to the left by a distance \(d_1\) relative to the water. In a second scenario, the same person stands at the left end of a flatboat of mass \(M_2 = 3m\) and length \(L\), also initially at rest on the water, and walks to the right end, causing the boat to shift to the left by a distance \(d_2\) relative to the water. What is the ratio \(\dfrac{d_2}{d_1}\)?

![A side-view diagram of a person standing at the left end of a flatboat floating on water. A horizontal straight line represents the calm water surface. Resting horizontally on this surface is a narrow rectangular block representing the flatboat of mass \(M\). A horizontal double-headed dimension arrow extends along the bottom of the boat from its left edge to its right edge, labeled \(L\). Standing upright at the far left edge on top of the rectangular block is a stylized figure of a person of mass \(m\). A horizontal arrow pointing to the right above the person indicates the direction of walking. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604289-9BfQqb.jpg)

- **A.** \(2\)
- **B.** \(\dfrac{7}{3}\)
- **C.** \(\dfrac{8}{3}\)
- **D.** \(3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124325/*