I agree with you, but the question states:
This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).
Therefore as the plane reaches full thrust and takeoff speed, the conveyor will be at the same speed.
So as the plane is being pushed forward by engine thrust, it is being pulled back by the conveyor. The wheels are simply spinning without actually going anywhere.
BUT:
At the same time, think of an aircraft carrier. If the carrier were moving East at the same speed the plane was trying to take off in a Westward direction, the plane would not have enough speed to take off, it would plummet into the ocean because it runs out of runway fster.
OK no
I got it this time.
Consider take off speed of a plane is 100knots.
Say the conveyor had a static speed of say 100knots. In order for the plane to reach 100knots it needs to use maximim thrust. At this point they are going the same speed and there is no displacement. In order for the plane to overcome the conveyor force, it will need to genereate more thrust. In essence it needs twice the speed to take off.
I don’t know, something to do with vectors right? I’ve hated physics since high school.