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A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.
Now, you on the rollerblades is the airplane, the treadmill is the conveyor belt, and you pulling the rope are the turbines. You will still move forward on the treadmill regardless of how fast the treadmill is going because of the external force moving you forward.