Question

A plane flying due north at 100 m/s is blown by a strong wind at 500 m/s due east. What is the plane's resultant velocity?

Answer 1

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

$$v_{res}=\sqrt{v_x^2+v_y^2}=\sqrt{(500\ \dfrac{m}{s})^2+(100\ \dfrac{m}{s})^2}=510\ \dfrac{m}{s}.$$

We can find the direction of the plane's resultant velocity from the geometry:

$$\theta=tan^{-1}(\dfrac{v_y}{v_x}),$$ $$\theta=tan^{-1}(\dfrac{100\ \dfrac{m}{s}}{500\ \dfrac{m}{s}})=11.3^{\circ}\ N\ of\ E.$$