Because this is important to the understanding of where infinity comes from, I'm going to label it in a bold font.
How the runaway-conveyor scenario works:
Setup 1:
Imagine the conveyor adjusts itself to the speed of the plane relative to the ground. This is the scenario where the wheels rotate at twice their normal speed.
Setup 2:
Imagine the conveyor adjusts itself to the speed mentioned above in setup 1 plus the reading on the plane's speedometer (which measures the speed relative to the conveyor itself). In this case, the conveyor quickly speeds up to infinity.
Anyway, that's where infinity comes from.
Nope, not part of the original problem statement. I believe you are injecting "info" simply to further the thread life.
There is an airplane on a runway. The runway is like a conveyor belt, and can detect the speed of the wheels of the airplane. When the runway senses the wheels moving, the runway will match the speed of the airplane's wheels, but in the opposite direction.
This specifies a theoretical gain by the speed sensor of exactly one with no reference to the airplane's relative ground speed. (Ground speed has no effect on air speed, which is what makes an airplane fly. Although encounters with the ground can preclude further flight, with or without injuries.) Anyway, there is no multiplication effect inherent in the problem statements. Conveyor speed response is stipulated as instantaneous. And the converor is presumably there in the first place, to insulate the airplane from the ground. There are no drag coefficients stated either. The whole exercise is theoretical. And, under these theoretical stipulations, infinite speed of the conveyor is only achieved when the plane wheels reach infinite speeds. Pretty sure take off would occur before that speed, which would preclude infinite speed all by itself. Further, what's the point of using an airplane in the problem statement if it needs infinite speed to achieve flight? Anyway, infinite speed is a theoretical concept, which only occurs in unproven theory.
Since the constructs of the problem are unreal. One can make the argument that the reasoning needed for solving an unreal problem must also be unreal. (Who can argue that this thread is anything but unreal?) But, with that logic, unrealistic speeds of infinity are acceptable, as well as an airplane the requires those speeds for flight. My assumption is that this thread continues due to some endorphin producing effect from mental masterbation.
I think the marine corps uses the phrase ClusterF*ck.
Oh Oh Oh Oh Aaaahhhh
By the way here is the airplane refered to in this thread:
Poll