No 5) Relative Motion calculations done properly:
Here is an example of a relative motion calculation.
Notice, when we do the calculations, that the INITIAL motion of the Earth, atmosphere and plane (on the ground), cancel out.
(See diagram No 5-1)

No 5-2) The plane and atmosphere stationary, relative to the ground.

No 5-3) The plane flying away from the airport, with no wind, relative to the airport.

No 5-4) The plane flying towards the airport, with no wind, relative to the airport.

No 5-5) The plain flying away from the airport with a wind, also going away from the airport.

No 5-6) The plane flying towards the airport with a wind going away from the airport, opposed to the plane.

No 5-7) The plane flying away from the airport, with a wind going towards the airport, opposed to the plane's direction.

No 5-8) The plane flying towards the airport with a wind, going in the same direction as the plane, towards the airport.

No 5b) Notice, regardless of the wind direction, or direction of the plane, one does not have to account for the velocity of the Earth.

That is already taken into account because, relative to the ground, the atmosphere and plane are already going in the same direction and speed.

*** The wind and plane direction are additions, relative to the ground. ***
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To take into account the ground's speed, is to be an observer in another frame of reference, e.g. in space, magically hovering above the Earth, exactly countering the rotation of the Earth.

This doesn't make sense in real life, because such a position would require an enormous amount of energy and force to keep it still relative to everything else.