Let me break this down for you the way it was told to me:
This is a very simplistic question with LOTS of variables missing, but we'll approach this from a theoretical standpoint.
quote:
A plane is standing on a movable runway(something like a conveyor).
Plane's speed (A)= 0
quote:
As the plane moves, the conveyor moves but in the opposite direction.
Plane movement (A). Conveyor Belt movement (B).
Now here's the key statement:
quote:
The conveyor has a system that tracks the speed of the plane and matches it exactly in the opposite direction.
Note that the statement says that the movement of the belt matches the speed of the plane EXACTLY. Now this could never happen in the real world, but in this answer, we have to assume those conditions. Therefore, Plane speed A. Conveyour belt (B) = -A.
So when the planes starts down the runway, the runway starts matching it's speed exactly. At 5 mph (plane speed), the belt is moving at 5 mph in the opposite direction. 5 + -5 = 0. So the plane thinks it's going 5 mph. The instruments wuold read that it's moving 5 mph, but because of the belt, it's not going anywhere. If the total speed of the system is 0, then there is no airflow, thus, there can be no flight.
This remains true no matter what the plane's speed. 250 mph + -250 mph = 0 total speed. Same at 500 or even 1000.
Given what we were told in the question, which isn't much, this is the only solution one can come up with. The plane never moves down the runway, even with engines wide open because the belt is matching speed EXACTLY and always has been.