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?

The relative velocity of the airplane with respect to the ground is 329.6 m/s.

The airplane's ground speed is faster than the airspeed because the relative speed of the the ground is zero causing the airplane to appear faster.

The given parameters;

The velocity of the airplane relative to the ground is calculated by applying Pythagoras theorem as follows;

Thus, we can conclude that the airplane's ground speed is faster than the airspeed because the relative speed of the the ground is zero causing the airplane to appear faster.

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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.