My official response is that there is not enough information in the question

Quote:
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?
Since the plane is standing on the runway the net movement would be 0 therefore the plane would not take off.

If the question assumes that the plane makes an effort to move forward and the treadmill matches spead of the fusalage..sp? then the plane would take off. The best explanation for this would be that there is a rope attached to the back of the plane that runs to a pulley that attaches to the front of the treadmill as plane moves forward the treadmill would turn back at exact speed that the plane moves forward.

If the treadmill is matching the speed of the plane based on the speed of the tires then the plane would remain static and would not take off .