Quote Originally Posted by mbeige View Post
Mathematically speaking, if the velocity of the plane were V, and the velocity in respect to the conveyor belt was -V (opposite in direction but having the same magnitude), then they will cancel each other out, so the plane will be stationary. The only way there will be lift is if there is wind going across the wings, and the only 2 ways to achieve it are by moving the plane forward (which does not happen) or by having a huge fan blow the air towards the plane to simulate its actual speed. Of course, the latter will not take off too, because it will just hover for a few seconds and eventually fall back to the ground (no momentum).
The velocity of the plane and the runway can't cancel each other out. Velocity is change in position, and the plane's position is independent of that of the treadmill este runway. Kung two equal but opposite "velocities" acting on the plane, saka sila magka-cancel out.

Now, if the question was that the runway will exert a force opposite that and acting on the airplane, then the plane will not move.

Pero kung speed lang nung runway ang pinaguusapan, lilipad yung eroplano.

At the moment of takeoff: Relative to the wind, airplane will be running at takeoff speed, the runway will be running at takeoff speed towards the other direction. Relative to each other, the plane and the runway will be passing each other at TWICE the take of speed.