A ship travels northward at $15,\text{km/h}$ while a river flows eastward at $10,\text{km/h}$. What is the ship’s resultant speed and its direction relative to the north?

Step-by-step solution

1. Add the velocity vectors: ${\mathbf{V}}_{\text{res}}=15\mathbf{j}+10\mathbf{i};$ (north as $\mathbf{j}$, east as $\mathbf{i}$).
2. Compute the magnitude: $|{\mathbf{V}}_{\text{res}}|=\sqrt{15^2+10^2}=\sqrt{325}\approx 18.0\text{km/h}$.
3. Find the direction angle east of north: $\theta ={\tan }^{-1}\frac{10}{15}\approx 33.7^{c}irc$.
4. State the resultant speed and direction.

Concept tested: Vector addition of velocities

Published 7 October 2026 · How this solution was prepared and checked