https://en.wikipedia.org/wiki/Cat_righting_reflex#Terminal_velocity"Terminal velocity" is the
maximum velocity of a body as it falls through air. Mathematically, the velocity at ground increases with the starting height, but beyond a certain height the increase is negligible.
The article says that (1) the terminal velocity for a cat is 100 km/h and (2) that velocity is pretty much attained when falling from 5-6 stories. One of these must be wrong, since a cat falling from 18 meters (6 generous stories) in vacuum would hit the ground at ~70 km/h only.
I would go with 8-10 stories.
A
veterinarians's paper cited in that WP article says:
Kapatkin and Matthiesen (1991) suggest that the type of injury depends upon the height of the fall and the landing surface. The severity of injuries rises linearly up to the seventh storey. After that height, the severity of injuries does not rise and and the incidence of fractures decreases. Of 22 cats that fell more than seven stories only one died, and among 13 cats that fell more than nine stories only one fracture was diagnosed. One cat that fell 32 stories suffered only mild pneumothorax and a chipped tooth (Whitney and Mehlhaff, 1987).
Robinson (1976)stated that the maximum recorded heights for survival were 18 stories on to a hard surface, 20 stories on to shrubbery, and 28 stories on to awning
So there seems to be some reason to think that cats reach terminal velocity at relatively low height (8-10 stories); that the terminal velocity is quite a bit less than 100 km/h, perhaps half of that; and that a cat could indeed survive a fall from the Empire State Building (if it does not die of boredom along the way
)
I do not think it would survive from the top of the state.
I have had this explained to me in some detail by a vet in the past, after an incident with a cat thrown out of a balcony type situation in Sydney (not my cat) and basically, they are fucked below a certain height, there is a sweet spot where they would survive, and then there is height from which if they fall, there is nothing that can stop the cats head, dipping, and they would most likely die.
But this is getting circular and I am not about to go and test this and when it comes down to it, I am not an expert in throwing cats off of a roof... beyond what I have been told by someone else... so I concede it could be wrong.. but that said, I would take a cash bet on this, and my bet would be kitty is fucked up beyond all repair from a flight off the empire state.