The problem is the animal drops away from the string, it cannot move faster than gravity can move it this is D = (iV * t) + (1/2a * t2) where t2 is time squared. iV is 0 so remove it.
1/2A * T2 = 1/2(9. * .293(.293) = .4m that means that at 40 yards if the animal reacts INSTANTANEOUSLY it can drop 16". Now if you figure in the fact that two things must happen, one the deer must hear the sound, and then react to the sound it is physically impossible for it to react instantaeously.
Humans(albiet slower have an average reaction time around .200) now take a highly trained individual at the peak of his reaction ability you are looking at a late teens early 20's individual with a reaction time of .160 for auditory reaction (http://biology.clemson.edu/bpc/bp/Lab/110/reaction.htm)
There is a limit to how fast a reaction can occur based purely on the biology of how impulses are sent. cut the reaction time of the human to 2/3 and you have a reaction time of .12 seconds. Now, you have a lapse time of sound being .293-.120, time of drop is now .173
4.9 * .173(.173) = .14m = .48 feet = 5.8" I have never shot a deer that had a chest less than 16'' deep. aim for the center of the deer and he drops 6'' your still gonna hit'em in the vitals.
Kirby