Question

The boat is heading due north as it crosses a wide river with a velocity of 10 km/h relative to water. The river has a maintain velocity of 5 km/h due east. Determine the velocity of the boat with respect to an observer on the riverbank.

Answer 1

We can find the magnitude of the velocity of the boat with respect to an observer on the riverbank from the Pythagorean theorem:

$$R=\sqrt{v_r^2+v_b^2}=\sqrt{(5\ \dfrac{km}{h})^2+(10\ \dfrac{km}{h})^2}=11.2\ \dfrac{km}{h}.$$

We can find the direction of the velocity of the boat with respect to an observer on the riverbank from the geometry:

$$\theta=tan^{-1}(\dfrac{v_r}{v_b}),$$ $$\theta=tan^{-1}(\dfrac{5\ \dfrac{km}{h}}{10\ \dfrac{km}{h}})=26.6^{\circ}\ N\ of\ E.$$