Question

A commercial ship is heading due North

at 12.0 km/hr but drifts westward at 5.0

km/hr. determine the magnitude and

direction of the resultant velocity of the

ship.

Answer 1

We can find the magnitude of the resultant velocity from the Pythagorean theorem:

$$v_{res}=\sqrt{v_x^2+v_y^2}=\sqrt{(5\ \dfrac{km}{h})^2+(12\ \dfrac{km}{h})^2}=13\ \dfrac{km}{h}.$$

We can find the direction of the resultant velocity from the geometry:

$$\theta=tan^{-1}(\dfrac{v_y}{v_x})=tan^{-1}(\dfrac{12\ \dfrac{km}{h}}{5\ \dfrac{km}{h}})=67.4^{\circ}\ N\ of\ W.$$