Not really helpful. I don’t have a vacuum chamber, let alone one 10 metres high. Nor the precision instruments to get accurate results. However, I am going to have a go anyway. But an experiment still won’t answer why, which is the question.

That’s true for a typical high school physics question. But that’s not my question here.

So ‘rebound rate’ is formally referred to as ‘coefficient of restitution’. Then the question could be, is the coefficient of restitution constant for a given ball? And if not, how does height in particular (or velocity on impact) affect the coefficient of restitution? I hadn’t considered sound, but in a vacuum that would be zero along with aerodynamic forces.

I do not have access to any undergraduate or higher physics textbooks.

If I understand correctly, the atomic matrix of the ball gains oscillation (energy), and since atoms are so small and many (and chaotic due to quantum effects?) that oscillation energy is unrecoverable as net kinetic energy (velocity of the ball) and dissipates randomly throughout (i.e. increased heat). Follow up question, is the % kinetic energy lost (to this heat) typically more or less for a higher velocity impact?

It is your “not necessarily so” that I need to explore more. So I will find out more about the $\pi$ theorem.

Although, is not energy more fundamental than temperature? For me, that opens a can of worms because of mass–energy equivalence in Einstein’s famous equation. But this equivalence, and distance—time equivalence (via relativity), don’t necessarily mean they are actually just different expressions of some more fundamental thing about the universe that can be measured. Or maybe it is, as @Ted Bunn suggests in the topic I linked—to my dissatisfaction. I think not. So maybe I can say that in the same way angle, although it has some equivalence to length, is also a fundamentally different measure.

@JohnForkosh Yes that is helpful. The systems of units on that page (e.g. Planck units) give everything in terms of length (m), time (s), mass (kg), temperature (K) and charge (C). So the “fundamental measures” then are length, time, mass, temperature and charge.

Speed needs a measurement of time and a measurement of distance, both time and distance being more fundamental measures than speed and speed being directly and exclusively constructed from them. Angle similarly needs two measures, but both of distance which cancel each other out, but only if you define angle as a ratio of orthogonally measured lengths. A sloppy way to say it but I mean like in a right triangle. But that reintroduces 90° tucked away in the assumed 2/3-dimensionality of space. So angle, while dimensionless in its units, must still be a “fundamental measure”.

Right. That makes sense. But angle in the physical world is something fundamentally different to measure than length. Even if you can make a construction with lengths to define any angle (in which the length units could cancel out, like in gradient) it is still a different thing to measure in the physical world.