Well, the truth is that 2,000 feet being covered by the horizon represents proof that the earth is flat. If only 2,000 feet remains covered by the horizon, the view is impossible on a round earth, but possible on a flat earth. The only explanation is air density over the water increasing, which results in a total mirage. This mirage bends light so it gives the appearance of it being hidden by the horizon.
You got that the wrong way around JJ, the denser air nearer the surface would actually be refracting the light downwards, so that would make more of the mountain visible, not less. If the earth were flat, the whole mountain would be visible from 100 miles away. Any amount being obscured is strong evidence for the round earth model.
Oh, and FlatOrange didn't say it was exactly 2,000ft that was obscured, he said "...at least 2,000 feet...".
For this reason, it is recommended that one rely on short distance measurement around 6 miles or so... This allows no large amount of surface area to create a mirage effect.
As I said, the general tendency is actually to make an object appear higher than it actually is, which means that measurements over any distance should be more supportive of the flat earth model. Instead, they are less, as I showed with my own mountain measuring experiment.
It is important to note that adding human eye level to the actual radius of earth creates a negligible difference in calculation. The earth's radius stands at 3,959 miles, so calculating the human height and converting it to miles gives a ridiculously small decimal number that interferes with calculation more than it helps...
The difference between using average human eye level and not using it is not entirely negligible. If you take line of sight from the surface, then you cannot see anything beyond a few feet away, if it is also at ground level. If you take line of sight from the average human eye level, then the viewable distance extends out to about 5km or so.