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

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