Well, that explains it - the little characters on the y-axis labels are 'h', not 'k', so I think you are reading it as three orders of magnitude too large
Doh! I know exactly what happened. That part was small and blurry, and in my initial scan over the graph, before I sorted out what the graph wa showing, it looked like "kp". A corner of my brain thought WTF is "kp", and I kept scanning elsewhere for information. I saw the speeds across the bottom and the thrusts on the left and I recognized the shape of the graph, then saw the HP vs MPH title at the top. I realized the different color lines had to be different engine inputs and I glanced back at that top-right box to confirm it.... that it was listing different HP engine inputs.... and that "k" from "kp" was still lingering in my brain. chuckle. So the blurry "h" was read twice, once as "k" and once as "h". The 250khp to 500khp power figures did strike me as unreasonably large, but I wasn't going to doubt the graph and my attention was absorbed on other issues. Sso without further consideration I just mentally filed it away as presumptively plausible values for a top end (?military?) engine.
the airflow through the propeller is slowed down... in this view the rotor is acting as a turbine, though a very unusual one in which the power is delivered through its thrust bearing, not by torquing the shaft.
Ohhhh noooooo! You didn't...... cry cry cry. LoL.
I follow your reasoning, and it is a kinda cool point, but oh jezus I wish you didn't make that analogy. The prop is NOT spinning as a turbine, and I know that you know that it's not spinning as a turbine, but someone is going to read what you wrote and think that one or both of us said it's a turbine. Newbies already have a hard time wrapping their heads around the idea that the prop is a fan. Any whiff of describing it as a turbine feeds badly into the exact "contradictory explanations" that set off alarm bells for you.
[the math/science] It's still at high-school level
I wish. You and I went to significantly above average highschools. The majority of U.S. highschool graduates only have one year of science, and it's generally something very generic like "Earth science" or something. It's only in the last few years that most highschools have moved to a two year science requirement, and even then, what percentage are going to include force-energy physics? I think the most common is a year of Bio, and even there most schools avoid or actively deny Evolution in that class :/
with regard to the exam question explanation. It says, correctly, that their formula implies that a totally inefficient device (alpha = 0) would travel at the wind speed.
What happened there is an entirely arbitrary and semi-self-contradictory cornercase crawling out of the simplifying assumptions. They started with a model of an ideal (frictionless) cart, and then to model a "real" cart they lumped together all losses... including rolling friction.... into one term alpha. They then set alpha to total energy loss... and they were still modeling that alpha on an ideal frictionless cart. They also silently and arbitrarily assumed wind drag *wasn't* zero, despite the opposite parallel assumption of zero rolling resistance. chuckle.