Question

3. An airplane is heading north with an airspeed of 325 m/s with a wind from the east at 55.0 m/s. What is the airplane's velocity relative to the ground? Is the airplane's ground speed faster or slowerthan its air speed? Why?​

Answer 1

Let a denote the airplane's velocity in the air, g its velocity on the ground, and w the velocity of the wind. (Note that these are vectors.) Then

a = g + w

and we're given

a = (325 m/s) j

w = (55.0 m/s) i

Then

g = - (55.0 m/s) i + (325 m/s) j

The ground speed is the magnitude of this vector:

||g|| = √[ (-55.0 m/s)² + (325 m/s)² ] ≈ 330. m/s

which is faster than the air speed, which is ||a|| = 325 m/s.