---
title: "A river with straight, parallel banks running east-west flows with a constant current velocity \\(\\vec{v}_{w/g}\\) directed due east. A boat travels with a constant speed \\(v_{b/w}\\) relative to the water, where \\(v_{b/w} > v_{w/g}\\). To travel in a straight line directly across the river from the south bank to a landing point on the north bank directly opposite the launch point, the boat must maintain a constant resultant velocity \\(\\vec{v}_{b/g}\\) directed due north. Which of the following vector diagrams correctly represents the relationship among the velocity vectors \\(\\vec{v}_{b/w}\\), \\(\\vec{v}_{w/g}\\), and \\(\\vec{v}_{b/g}\\)?"
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url: "https://nerd-notes.com/ubq/120518/"
date_modified: "2026-08-23T04:39:27+00:00"
---

# A river with straight, parallel banks running east-west flows with a constant current velocity \(\vec{v}_{w/g}\) directed due east. A boat travels with a constant speed \(v_{b/w}\) relative to the water, where \(v_{b/w} > v_{w/g}\). To travel in a straight line directly across the river from the south bank to a landing point on the north bank directly opposite the launch point, the boat must maintain a constant resultant velocity \(\vec{v}_{b/g}\) directed due north. Which of the following vector diagrams correctly represents the relationship among the velocity vectors \(\vec{v}_{b/w}\), \(\vec{v}_{w/g}\), and \(\vec{v}_{b/g}\)?

A river with straight, parallel banks running east-west flows with a constant current velocity \(\vec{v}_{w/g}\) directed due east. A boat travels with a constant speed \(v_{b/w}\) relative to the water, where \(v_{b/w} > v_{w/g}\). To travel in a straight line directly across the river from the south bank to a landing point on the north bank directly opposite the launch point, the boat must maintain a constant resultant velocity \(\vec{v}_{b/g}\) directed due north. Which of the following vector diagrams correctly represents the relationship among the velocity vectors \(\vec{v}_{b/w}\), \(\vec{v}_{w/g}\), and \(\vec{v}_{b/g}\)?

![A top-down view showing two horizontal parallel lines representing the south bank at the bottom and north bank at the top of a river. Between the banks, three rightward horizontal arrows indicate the water flow, labeled \(\vec{v}_{w/g}\). On the south bank, a filled circle marks the launch point labeled P. Directly opposite point P on the north bank, an open circle marks the destination point labeled Q. A vertical dashed line connects point P to point Q perpendicular to both banks. A four-point compass rose in the upper right corner shows North pointing upward and East pointing to the right. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459966-KKtaG8.jpg)

- **A.** Diagram A
- **B.** Diagram B
- **C.** Diagram C
- **D.** Diagram D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120518/*