---
title: "A boat can travel at a constant speed of \\(5.0 \\text{ m/s}\\) relative to the water. The boat is used to cross a river where the current flows at a constant speed of \\(3.0 \\text{ m/s}\\) relative to the riverbank. In order to travel along a path that is exactly perpendicular to the riverbank, the pilot aims the boat at an angle upstream. What is the magnitude of the boat’s velocity relative to the riverbank?"
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url: "https://nerd-notes.com/ubq/113921/"
date_modified: "2026-06-22T07:38:24+00:00"
---

# A boat can travel at a constant speed of \(5.0 \text{ m/s}\) relative to the water. The boat is used to cross a river where the current flows at a constant speed of \(3.0 \text{ m/s}\) relative to the riverbank. In order to travel along a path that is exactly perpendicular to the riverbank, the pilot aims the boat at an angle upstream. What is the magnitude of the boat’s velocity relative to the riverbank?

A boat can travel at a constant speed of \(5.0 \text{ m/s}\) relative to the water. The boat is used to cross a river where the current flows at a constant speed of \(3.0 \text{ m/s}\) relative to the riverbank. In order to travel along a path that is exactly perpendicular to the riverbank, the pilot aims the boat at an angle upstream. What is the magnitude of the boat's velocity relative to the riverbank?

![A top-down view of a river with parallel banks. A vector labeled v_WG points to the right (downstream) with a magnitude of 3.0 m/s. A boat on the lower bank is oriented at an angle pointing upstream (to the left and across). A vector labeled v_BW represents the boat relative to the water with a magnitude of 5.0 m/s. A vertical dashed line indicates the intended path directly across the river, perpendicular to the current.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1782113904-0qfHKn.jpg)

- **A.** \(2.0 \text{ m/s}\)
- **B.** \(4.0 \text{ m/s}\)
- **C.** \(5.8 \text{ m/s}\)
- **D.** \(8.0 \text{ m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113921/*