---
title: "Two long, perpendicular conveyor belts lie in the horizontal plane of a factory floor. Belt 1 moves due east (\\(+x\\)-direction) at constant speed \\(v_0\\) relative to the floor. Belt 2 moves due north (\\(+y\\)-direction) at constant speed \\(2v_0\\) relative to the floor. A motorized robotic module \\(M\\) moves across Belt 1. A sensor mounted on Belt 2 tracks module \\(M\\) and measures its velocity relative to Belt 2 to be directed due west (\\(-x\\)-direction) with magnitude \\(v_0\\). Which of the following expressions correctly gives the speed of module \\(M\\) relative to the factory floor, \\(v_{M/F}\\), and the speed of module \\(M\\) relative to Belt 1, \\(v_{M/1}\\)?"
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url: "https://nerd-notes.com/ubq/119094/"
date_modified: "2026-08-18T04:48:51+00:00"
---

# Two long, perpendicular conveyor belts lie in the horizontal plane of a factory floor. Belt 1 moves due east (\(+x\)-direction) at constant speed \(v_0\) relative to the floor. Belt 2 moves due north (\(+y\)-direction) at constant speed \(2v_0\) relative to the floor. A motorized robotic module \(M\) moves across Belt 1. A sensor mounted on Belt 2 tracks module \(M\) and measures its velocity relative to Belt 2 to be directed due west (\(-x\)-direction) with magnitude \(v_0\). Which of the following expressions correctly gives the speed of module \(M\) relative to the factory floor, \(v_{M/F}\), and the speed of module \(M\) relative to Belt 1, \(v_{M/1}\)?

Two long, perpendicular conveyor belts lie in the horizontal plane of a factory floor. Belt 1 moves due east (\(+x\)-direction) at constant speed \(v_0\) relative to the floor. Belt 2 moves due north (\(+y\)-direction) at constant speed \(2v_0\) relative to the floor. A motorized robotic module \(M\) moves across Belt 1. A sensor mounted on Belt 2 tracks module \(M\) and measures its velocity relative to Belt 2 to be directed due west (\(-x\)-direction) with magnitude \(v_0\). Which of the following expressions correctly gives the speed of module \(M\) relative to the factory floor, \(v_{M/F}\), and the speed of module \(M\) relative to Belt 1, \(v_{M/1}\)?

![Top-down view of two perpendicular conveyor belts on a grid labeled x and y. Belt 1 is aligned horizontally along the x-axis, with a rightward arrow labeled v_0 indicating its motion due east. Belt 2 is aligned vertically along the y-axis, with an upward arrow labeled 2v_0 indicating its motion due north. A square robotic module labeled M is positioned on Belt 1. Axes in the lower-left corner indicate the +x direction to the right and +y direction upward. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787028531-OF00rb.jpg)

- **A.** \(v_{M/F} = \sqrt{3}v_0\) and \(v_{M/1} = \sqrt{2}v_0\)
- **B.** \(v_{M/F} = \sqrt{5}v_0\) and \(v_{M/1} = 2v_0\)
- **C.** \(v_{M/F} = 3v_0\) and \(v_{M/1} = 2v_0\)
- **D.** \(v_{M/F} = \sqrt{5}v_0\) and \(v_{M/1} = 2\sqrt{2}v_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119094/*