Quote Originally Posted by Ruiner
Listen, this is rather simple:

No matter what the speed on the treadmill is in reverse (5mph, 10mph, 40mph, 150mph, etc), the plane will take off at its take-off speed.

Remember, the treadmill has to be as long as a normal runway.

Just watch. Notice how the plane travels forward? Eventually it would build up enough speed.
http://www.youtube.com/watch?v=-EopVDgSPAk
I can't watch the video, I'm browsing from my phone.

My point is that the plane will never reach any speed according to the OP. I would agree with you if the treadmill were at at constant speed.

If the treadmill continues to move underneath the aircraft, the plane will never move. It does not matter how a plane's forward momentum is normally achieved, it cannot go forward if the ground below it is moving in the opposite direction.