Gravity? That's only part of the story. We ain't shootin' in no stinkin' vacuum! You've got to factor in wind resistance!
Wind resistance increases at a faster rate with speed than KE does (velocity^3 for wind resistance of a subsonic object vs velocity^2 for KE). It takes more energy for an arrow traveling 300 fps to fight it's way through the atmosphere and make it to a 60 yard target than it takes for the same arrow traveling only 250 fps.
Use a lighter weight arrow to get it up to 300 fps and you start out with less energy from the bow. Since it starts out with less energy to begin with and uses up it's more of it's already depleted energy simply cutting thru the air on the way to the target, it's pretty easy to see how it's trajectory can deteriorate downrange at a faster rate than the heavier arrow.
Like the shockwave from this airplane, an arrow produces a shockwave. The faster the arrow is going, the more vertical the wave and the more resistance. The slower it's going, the more angled the wave and the less resistance.
I've just got a basic grasp at how this works and don't fully understand the whole thing. So, I wonder if any physicists with specialties in thermodynamics, fluid dynamics and aeronautics would care to take a stab at explaining it to us science dropouts?
