An american football has a drag coefficient of about .2, and a 4 oz projectile weighs 1750 grains. I plugged these factors into a ballistic calculator with a 500 f/s initial velocity (the calculator's minimum) and it spat out the attached. Note the 1044 inch drop at 400 yards, equivalent to about 87 feet.
https://www.vcalc.com/wiki/vCalc/Ballistic+Range This calculator gives an absolute maximum of 589 meters of flight with 45 degrees and 249 f/s without drag or other effects, which would be considerable with any projectile, especially with a diameter of about an inch and football shape's coefficient of drag.
I don't think these numbers calculated here are quite reasonable, as a .45 ACP is also listed in the tables as having about 350 ft-lbs of muzzle energy. That's a pretty good amount for a handgun.
Part of the issue is we need a very specific range, not measured in miles, to get this down properly, along with the ballistic coefficient, and a bunch of other data. As the longest recorded shots are all bracketing this range of 400-500 meters, with specialized projectiles having extremely good ballistics, I think there needs to be some more exact measurement before we ascribe velocities and "muzzle" energy to anything.
Someday I'll not be in grad school anymore, and have time to build an online slinging ballistics calculator...
https://en.wikipedia.org/wiki/Ballistic_coefficienthttps://web.archive.org/web/20120920043403/http://slinging.org/index.php?page=sl...http://baseball.physics.illinois.edu/clanet/ClanetSportsBallistics.pdf https://doi.org/10.1016/j.proeng.2012.04.018 Drag of american footballs.
https://www.jbmballistics.com/cgi-bin/jbmtraj_simp-5.1.cgi Ballistic Calculator
https://en.wikipedia.org/wiki/.45_ACP