Brainteaser Options

[james]

Here's a question for you:

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

A couple of links discussing it (and some funny rationalizations for peoples incorrect assumptions):
www.kottke.org/06/02/plane-conveyor-belt
www.straightdope.com/columns/060203.html

[james]

Another version to help you visualise the solution:

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. It doesn't matter how fast the treadmill ends up, your still pulling, the ropes still getting shorter and you will be getting closer to the wall.

As Cam rightly says the action of the conveyor & wheels is irrelevant and does not counteract the forward motion of the plane relative to the earth because you have an external force (the engines) providing that motion.