Question

A plane heads east with a veloncity of52m/s through a12m/s cross wind blowing the plane south find the magnitude and direction of the planes resultant veloncity (relative to due east)

Answer 1

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

$$R=\sqrt{v_p^2+v_w^2}=\sqrt{(52\ \dfrac{m}{s})^2+(12\ \dfrac{m}{s})^2}=53.4\ \dfrac{m}{s}.$$

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

$$\theta=cos^{-1}(\dfrac{v_p}{R})=cos^{-1}(\dfrac{52\ \dfrac{m}{s}}{53.4\ \dfrac{m}{s}})=13^{\circ}\ S\ of\ E.$$