ORIGINAL: GMMAT
How do you know how fast the arrow is traveling when it gets to the yardages you cite?
The arrow leaving a bow at 270 feet per second will slow down the further from the bow it gets, but when you are speaking of fractions of a second, I don't believe the drop in speed will be that measurable for the average person. For every arrow weight the terminal velocity and then the rate of decent would be different.
All I was saying after doing the math was that is FAST for a deer to hear the sound of the bow shot and react.