Although I have never killed anything past 40 yards, I go afield prepared to shoot out to twice that far. One thing you will find with arrows is that the propensity for an animal to jump the string goes down quite a bit beyond 40 or 50 yards. I'm sure they hear it, but it doesn't seem to trigger the alarm response like a sound inside their "red" zone.

They can, however, sometimes see the arrow flying towards them. I had an antelope buck jump an entire body length as my arrow was streaking towards him, at 75 yards, last year. I also had a turkey dodge an arrow at 25 yards once. He didn't seem to even see it coming until it was about 1/2 way there, and still managed to just barely get out of the way. Moral of story: wait until they look away before letting the arrow fly.