Or
Speed of Wheels - Speed of Conveyor = Speed of Plane
In the statement of question, Francisco stated:
"The conveyer belt is designed to exactly match the speed of the wheels
at any given time, moving in the opposite direction of rotation."
He did not state the speed of the aircraft, but the speed of the wheels.
Given the formula above the forward speed of the plane should always be
zero and can not generate enough lift to takeoff.
is the viewpoint im taking on this. (googled it).
If the treadmill is intended to match the speed of the airplanes wheels at every moment, then frictionless wheel bearings mean naff all. Wheels will be spinning... treadmill will be spinning just as fast. To someone standing outside the treadmill plane system it will appear stationary, onboard ground speed will be sky high, yet airspeed will also be 0.
Airspeed is what allows the plane to take off. NOT GROUND SPEED. So... there.
Edit:
Or in your words, in relation to the ground (treadmill) the plane will be moving at mach 2. in relation to the air, itll be stationary.