---
title: "An aerial research drone flies in a region with a constant, uniform horizontal wind. On a first test run, the drone is steered due North with an airspeed of \\(65\\text{ m/s}\\), and tracking instruments indicate its ground track is directed at an angle \\(\\theta_1\\) East of North, where \\(\\tan\\theta_1 = 0.25\\). On a second test run, the drone is steered due East with an airspeed of \\(55\\text{ m/s}\\), and its ground track is directed at an angle \\(\\theta_2\\) North of East, where \\(\\tan\\theta_2 = 0.20\\). What is the speed of the wind relative to the ground?"
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url: "https://nerd-notes.com/ubq/124137/"
date_modified: "2026-09-28T13:30:38+00:00"
---

# An aerial research drone flies in a region with a constant, uniform horizontal wind. On a first test run, the drone is steered due North with an airspeed of \(65\text{ m/s}\), and tracking instruments indicate its ground track is directed at an angle \(\theta_1\) East of North, where \(\tan\theta_1 = 0.25\). On a second test run, the drone is steered due East with an airspeed of \(55\text{ m/s}\), and its ground track is directed at an angle \(\theta_2\) North of East, where \(\tan\theta_2 = 0.20\). What is the speed of the wind relative to the ground?

An aerial research drone flies in a region with a constant, uniform horizontal wind. On a first test run, the drone is steered due North with an airspeed of \(65\text{ m/s}\), and tracking instruments indicate its ground track is directed at an angle \(\theta_1\) East of North, where \(\tan\theta_1 = 0.25\). On a second test run, the drone is steered due East with an airspeed of \(55\text{ m/s}\), and its ground track is directed at an angle \(\theta_2\) North of East, where \(\tan\theta_2 = 0.20\). What is the speed of the wind relative to the ground?

![Two side-by-side vector diagrams labeled Run 1 and Run 2. At the top left, a four-point compass rose indicates North pointing vertically upward and East pointing horizontally to the right. In the left panel labeled Run 1, a dashed vertical reference line extends upward from an origin point. A solid arrow labeled v_1 points vertically upward along this line. A second solid arrow representing ground track begins at the same origin and extends upward and slightly to the right, forming an acute angle labeled \theta_1 with the vertical dashed line. In the right panel labeled Run 2, a dashed horizontal reference line extends to the right from an origin point. A solid arrow labeled v_2 points horizontally to the right along this line. A second solid arrow representing ground track begins at the same origin and extends to the right and slightly upward, forming an acute angle labeled \theta_2 with the horizontal dashed line. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602238-73xp7I.jpg)

- **A.** \(10\text{ m/s}\)
- **B.** \(15\text{ m/s}\)
- **C.** \(20\text{ m/s}\)
- **D.** \(25\text{ m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124137/*