Can a Plane on a Treadmill Take Off?

....continue my previous post
TAILWIND equal to x MPH:
*Assume a tailwind has suddenly come up! Suddenly means that the plane
didn't have time to react to it and since the tailwind equals Vlof this
means that your entire true airspeed drops away! So airspeed now is 0!
But your groundspeed for the moment remains x MPH as in previous case
and so does the tirespeed/tredmill speed which is 2x.
Briefly:
GS=x TAS=0!
Tirespeed=2x plane would not anymore takeoff!! WINDSHEAR,
WINDSHEAR!! Dangerous condition which can happen in real life!

*Now assume the plane has overcome the tailwind and the airspeed has
recovered and is again equal to x MPH. Good! Now the groundspeed will
be 2x and the tirespeed 3x! Because vector 2 is counteracted by an
opposite and equal in magnitude wind vector, there is now a new vector
4 (see drawing previous post). Oh God, maybe I should have drawn that
sketch a little differently! I'm not going to go through all this
again. Anyway, would you now do me a favor and CLOSE THE DISCUSSION
PLEASE!!

In short, the article from the first post is correct! End discussion,
"point final", over and out!!

PS:If you would like to know, I'm an engineer and an airline pilot!
Jeeeeezus!