---
title: "In an automated facility, Conveyor Belt 1 moves eastward at a constant speed \\(v_1\\) relative to the factory floor, while Conveyor Belt 2 moves northward at a constant speed \\(v_2\\) relative to the factory floor. A robotic actuator on Belt 1 launches a package across Belt 1 such that the package moves northward at a speed \\(u\\) relative to Belt 1. Which of the following expressions represents the speed of the package as measured by an observer moving with Conveyor Belt 2?"
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url: "https://nerd-notes.com/ubq/119057/"
date_modified: "2026-08-18T04:47:13+00:00"
---

# In an automated facility, Conveyor Belt 1 moves eastward at a constant speed \(v_1\) relative to the factory floor, while Conveyor Belt 2 moves northward at a constant speed \(v_2\) relative to the factory floor. A robotic actuator on Belt 1 launches a package across Belt 1 such that the package moves northward at a speed \(u\) relative to Belt 1. Which of the following expressions represents the speed of the package as measured by an observer moving with Conveyor Belt 2?

In an automated facility, Conveyor Belt 1 moves eastward at a constant speed \(v_1\) relative to the factory floor, while Conveyor Belt 2 moves northward at a constant speed \(v_2\) relative to the factory floor. A robotic actuator on Belt 1 launches a package across Belt 1 such that the package moves northward at a speed \(u\) relative to Belt 1. Which of the following expressions represents the speed of the package as measured by an observer moving with Conveyor Belt 2?

![Top-down view of two perpendicular conveyor belts on a factory floor. Conveyor Belt 1 is horizontal, extending along the x-axis, with a rightward vector arrow labeled \vec{v}_{1/F} pointing east. Conveyor Belt 2 is vertical, extending along the y-axis, with an upward vector arrow labeled \vec{v}_{2/F} pointing north. A rectangular package sits on Conveyor Belt 1. An upward vector arrow starting at the package is labeled \vec{v}_{P/1}. A dashed coordinate axis set sits in the corner with x pointing east and y pointing north. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787028433-AROtMk.jpg)

- **A.** \(\sqrt{(v_1 - v_2)^2 + u^2}\)
- **B.** \(\sqrt{(v_1 + v_2)^2 + u^2}\)
- **C.** \(\sqrt{v_1^2 + u^2 + v_2^2}\)
- **D.** \(\sqrt{v_1^2 + (u - v_2)^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119057/*