if the belt matched the speed of the plane it would not take off. Air needs to move over the wing with enough velocity for the preesure below the wind to be greater then the pressure above. the jet engine does nothing but push the plane forwards to create said air velocity. if you are running on a treadmill, do you feel the wind in your face?
If the belt matches the rotational speed of the wheels, the plane cannot take off.
If the belt matches the speed of the plane, the plane can take off.
The reason? The plane has to move forward relative to the air around it, and it can only do this by moving forward on its wheels.
Remember, this is a theoretical question, not a practical one. There have been a lot of debates, but on a BB that consists of airline pilots, engineers, and mechanics, they all agreed that the plane would not take off and also that the question is poorly worded.
Hey GB - if a conveyor is moving backwards at the same speed as the wheels are rotating forward, then the wheel itself can't move forwards. Mythbusters will, of course, miss this fine point, try to take off a plane from a conveyor belt without this limitation, and pat themselves on the back.
Their question is worded differently, and the way it is worded, the plane can take off. I bet this is what they will find.
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