If this Board were a bar I can envision drunken fisticuffs over an inane issue. The deciding point of this issue is not based in physics but legal interpretation.
First, we start with the problem statement:
"A plane is standing on a runway that can move (like a giant conveyor
belt). This conveyor has a
control system that tracks the plane's
speed and tunes the speed of the conveyor to be exactly the same (but
in the opposite direction).
Will the plane be able to take off?"
The plane has speed so we can assume it's engines are on giving rise to the speed. "Tracking the plane's speed" implies that the plane's velocity is measured against a reference point not attached to the plane or the conveyor. Logically this would be the ground. The control system then commands the conveyor to move at the same speed but in the opposite direction to the plane.
When a plane takes off under normal conditions, (take off roll) the ground underneath the plane always moves at the same speed as the plane but in the opposite direction of the plane. This apparant motion is the same as the conveyor.
Therefore the conveyor does nothing more than a runway. The plane will take off.
