Answer to Question #259099 in Physics for Martin

Question

An airplane's compass indicates that it is headed due north and its airspeed indicator shows that it is moving through the air at 240 km/h. If there's a 100 km/h wind from west to east, what is velocity of the airplane relative to earth?

Answer 1

The magnitude of the velocity can be found by Pythagorean theorem:

$$|v|=\sqrt{240^2+100^2}=260\text{ m/s}.$$

The angle from East toward North is

$$\theta=\arctan\frac{240}{100}=67°.$$