I don' t know about your test or your math wizard, but MY calculator says you' re wrong.

The speed of gravity is 32.16 fps^2. That' s right at 386 inches per second. Just relying on gravity alone, a deer could drop 20" in .052 second.

An arrow traveling 345 fps would take a solid .174 second to travel 20 yards, .261 second to travel 30 yards and .348 second to go 40 yards. And that' s assuming a constant 345 fps and not even taking air resistance into account! The actual flight time is longer. The deer can duck clean under your arrow AT LEAST 3 times faster than your 345 fps arrow can get to it.

My calculator says to get that 345 fps arrow into that deer before it can drop 3 1/4" , you' d need to be shooting from 1 yard away.