I admit I didn't read all 52 pages, just 15, so maybe it was mentioned in the remaining pages, but I just want to add a few things.

Definitions
  • wind speed: speed of the air relative to the plane, 100mph wind speed means the wind is moving 100mph across the wings.
  • Global Perspective: This is the perspective being observed from the outside world, an example would be some one not standing on the tread mill watching the plane try to take off
  • Scenario perspective: Perspective from the plane, relative to the treadmill
  • Relative speed: speed of the treadmill as observed from the Scenario perspective, aka the plane
  • Absolute speed: speed of the treadmill as observed from the Global perspective.

Assumptions
  1. conveyor belt only moves the ground below the plane, not the air around the plane, and moves in the opposite direction the plane is trying to move.
  2. weather is ideal and wind is calm (0MPH).
  3. group speed = air speed since the plane is on the ground.
  4. wheels are freewheeling, ie there is little if any rotational friction between the wheel and the object it is attached to.
  5. plane would be able to take off if the tread mill was kept stationary.

Facts
  1. lift if determined by the wind speed over the wings.
  2. Thrust produced by the engines (prop or turbine) applies a force against the air.
  3. Thrust is dependent on wind speed, the higher the wind speed the lower the thrust, and vice versa.
  4. Force from the thrusters is what propels the plane and not the wheels.
  5. air is a fluid

ProofThe tread mill doesn't effect the speed of the wind:
Lets just say for the sake of argument that the tread mill does move the air around the plane at the same rate as the treadmill. If the plane is trying to go down the run way and is stationary from the global perspective the the wind will increase in speed as it passes over the wings. This equivalent wind speed will cause enough lift for the plane to take off, this scenario is essentially the same as if it was going down a normal run way. So we know that the tread mill does not effect the planes air speed because if it did it would be able to lift off.

If we look at a force diagram, the engines produces thrust forward by "throwing" air backwards and pushes against the air already present which produces a force pointing in the forward direction, this is because of newtons third law, equal and opposite reaction. So a force backwards produces a force forwards. The ONLY way for the plane to stand still from the global perspective is to have another force applied to the plane that would counter act this forward force, other wise the plane will move forward since F=ma (Force = mass X acceleration). Here are some possible options that could produce the required force to prevent:
  1. Air resistance, which is determiend by surface area and wind speed
  2. Excessive friction between the plane and the ground, for example Wheel Brakes are applied, or wheels are not present wheels.
  3. Plane is chained to a solid anchor

As seen by the fact that a high enough wind speed would creates lift and allow the plane to take off we can rule out wind, as enough wind the keep the plane stationary would surely allow it to take off.

Now if we make the assumption that the plane would be able to take off if the treadmill is kept still like a normal run way we can safely assume that plane has little resistance relative to the force generated by the thrusters. And that there is nothing nothing else binding the plane such as it being anchored. So we are safe to assume the airplane is not held by any external constraints.

Plus we know the wheel brakes are not applied because otherwise the plane would not be able to move anyways and the question is a trick question smile

So without any kind of constraints it is impossible for a plane to not move from a global perspective when it is at full throttle because there is no resistance to the forward force and because thrust and wind speed are inversely proportional therefor there will be a force acting on the plane moving it forward increasing the wind speed over the wing allowing for take off.

... In summary
The planes method of propulsion acts on the global perspective and not on the relative perspective allowing it to move in the global perspective as well, even if the wind was acted form a relative perspective it would be able to take off since it would have a high enough wind speed.

so yeah, the plane can take off regardless...