[Letum]

ok...here is the confusion.....


If the conveyor is moving back at the same speed that the plane is moving forward, then the plane will take off as normal. (assuming the wheels can withstand 2x takeoff speed.)
The events look like this:

1) Throttle is applied
2) Plane moves foward
3) Conveyor moves at speed of plane
4) Wheels spin at twice the speed of the plane
5) Plane continues to accelerate and take off


If the conveyor is moving back at the same speed that the plane's wheels are moving forward, then a loops forms. The loop looks like this:

1) Throttle is applied
2) Wheels move forward
3) Conveyor moves at speed of wheels
4) As before, the wheels must move twice as fast as the conveyor for the plane to move forward, so the wheels speed up
5) Conveyor speeds up to speed of wheels
7) As before, the wheels must move twice as fast as the conveyor for the plane to move forward, so the wheels speed up
8 ) Conveyor speeds up to speed of wheels
9) As before, the wheels must move twice as fast as the conveyor for the plane to move forward, so the wheels speed up
10) Conveyor speeds up to speed of wheels

This theoretically continues until friction breaks the wheel bearings. This will happen instantly because the wheels will (theoretically) instantly try to achieve an infinite rate of spin.
This is happening because for a plane to move up a conveyor moving at 100mph, it's wheels must move at 200mph, but if the conveyor is matching the speed of the wheels, the wheels can never double the speed of the conveyor, but the wheels must travel at twice the speed of the conveyor for the plane to move forward. All the energy of the plane's forward thrust is used in the friction of the wheel bearings. Even with perfect, zero friction, bearings that don't burn out, you will just get infinite wheel spin speed.
That's hard to understand because we never see any kind of system like that in the real world. It's not possible.

The riddle should read:


"There’s a plane on a magical threadmill runway. The threadmill defies
the laws of physics and can rotate as fast as the plane [CUT] is moving
in the opposite direction. If the plane rolls forward at 10 mph, the runway
underneath rolls backwards at 10 mph. The plane [CUT] moves up to 200 mph
and the runway rolls back at 200 mph. The question is, will the plane move
forward and take off or remain stationary?
If you had to think about it for even a second, you need to read this chapter.
The answer of course is yes, the plane will take off as normal."

The problem is that this isn't much of a riddle as it tells us that the plane is moving at 200mph.