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Sqrl said:
Uhm ok...wait...

Is the plane actually moving at takeoff speeds relative to the air or only relative to the treadmill? If the plane is only moving at takeoff speed relative to the treadmill its not going anywhere.

If the treadmill is going <----- at 200 mph and the plan is going ----> at 200mph + takeoff speed it will takeoff.

The actual situation needs to be properly defined.

 See that's the problem it's impossible to test because there is no way the treadmill will hold the plane stationary.