Question

An airplane flies at 500km/h in a 100km/h wind. What is the velocity of the plane relative to the ground?

Answer 1

I suppose the velocity 500 km/h is given relative to the air, and 100 km/h is relative to the ground. Then the velocity of the plane relative to the ground is:

$$\mathbf{v}_{plane\_ground} = \mathbf{v}_{plane\_air} + \mathbf{v}_{air\_ground}$$

where $|\mathbf{v}_{plane\_air}| = 500km/h, |\mathbf{v}_{air\_ground}| = 100km/h$. The actual value of $\mathbf{v}_{plane\_ground}$ depends on the angle between the plane and wind directions.