Good question,
but understand that there is something like inertia which have to be considered.
Why do you think a ball thrown straight up falls straightly down to our hands.If we take things as you said the ball has to fall somewhere else,by the time it is in air it has to reach a distance that is equal to the distance earth rotates in the same time.This doesnt happen in real because the ball also goes along with the rotation of earth (due to inertia) in such a way that the ball will fall back to our hand.
Similarly in case of aeroplane, if the plane is going opposite to the rotation of earth it actually is going in that direction.
But theres also possibility for the case you said.Like what if they are same?Is it in motion or rest.?
A body can be said to be at rest or motion with reference to the frame we consider.So the aeroplane is at rest with respect to the earth.Because the aeroplane is being on the exact same spot above earth.But with respect to someone in space, the aeroplane is in motion.
Hope this helps :)