The Acceleration of gravity is 32.16 ft/s^2 This is not a velocity it is the first derivative of the velocity equation and the second derivative of the position equation.
If we use equations from physics describing objects in free fall we need to look at the position equation (simplified for our purposes) y = (0.5)*g*t^2 that is how far the object (in feet) will fall in a given time t. The velocity component (simplified) of that is v = g*t this is how fast the object is falling (in feet/second) in given time t.
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.
I agree with the above calcs.
Just relying on the acceleration of gravity in order for the deer to drop 3.25in or .27ft it would take 0.13 seconds.
In order for his arrow (at 345 feet/second) to get to target before the deer dropped 3.25in (just relying on gravity to drop the deer) he would have to shoot from a distance of 44.85 feet or roughly 15 yards.
All of this is assuming
- The arrow travels in a straight line.
- The arrow has no loss in velocity due to air resistance.
- The deer only falls due to the acceleration of gravity.
- Newton is correct.
Don’t even get me started on the momentum issue.