HAY /sci/, logic problem!

There is a giant, 10 mile long stetch of runway with a 747 on the middle of it. The runway, however, is specially designed to move, much in the same way that a treadmill will move, in the opposite direction of the plane. Secondly, the treadmill is attached to a computer which will match the acceleration of the plane exactly and constantly, in the opposite direction.

What is the result of this experiment? Does the plane ever take off?

>>62
Oh my god, you're failing so hard.
Listen:
The plane moves forward with velocity v(t) (along the tread) at time t. The computer controls the treadmill so that the velocity of the portion of the tread under the plane at time t is -v(t). The tread is finite and you'd run into problems at/near the end of the tread, but that doens't matter since if the plane is moving it would take off long before then.

Furthermore, even if it was actually the whole treadmill - and not just the belt - moving backwards, the plane would still take off for exactly the same reason. More generally, the movement of the ground doesn't matter (except as an engineering problem because of possible high heat from friction and such) unless the vehicle accelerates by using an engine to rotate its wheels, as a car does. If it uses a jet engine or a propeller, the wheels will simply move faster to account for the movement of the ground.