Scenario: An elf ranger with proficiency in the longbow, 16 DEX and the Sharpshooter feat prepares to shoot an arrow from her bow. A halfling wizard is positioned about 30 feet in front of the ranger and has readied a reduction spell to be cast on the arrow as it flies over his head.
The details on a Longbow are (PHB 149):
Longbow - 50 gp - 1d8 piercing - 2 lb. - Ammunition (range 150/600), heavy, two-handed
When the arrow flies over the halfling's head he casts the reduction spell and per the rules on Enlarge/Reduce (PHB 237):
The target’s size is halved in all dimensions, and its weight is reduced to one-eighth of normal.
Question: Will this arrow travel 4800 ft?
The answer may depend on whether the velocity of the arrow remains constant or the momentum of the arrow remains constant, and probably other factors as well (?).
Velocity: If the arrow maintains it's current velocity it will continue to travel at the same speed and will lose momentum. Momentum = mass x velocity (p=mv), so if the speed stays the same and the mass is reduced the momentum is also greatly reduced. In this situation, assuming the arrow weighs 20 grams and is traveling at 60 m/s it would look like:
original: p=.02 x 60, p=1.2 after reduction: p=.0025 x 60, p=.15
Momentum: If the arrow maintains its current momentum its speed will increase dramatically after it is reduced in size. Again, momentum is related to both velocity and mass. With the same numbers as above, keeping the momentum constant and changing the mass to 1/8 we would have:
original: p=.02 x 60, p=1.2 after reduction: 1.2=.0025 x v, v=480 m/s
Because the mass is reduced to 1/8 the original, the speed increases by a factor of 8. The reduced arrow is now traveling at 480 meters per second which is faster than some bullets (and also slower than many, it's on the slow end). The weight of the arrow is also about that of a small bullet. For context 480 m/s = 1575 fps = 1074 mph.
If the momentum does remain constant does this mean the mini-arrow will now travel 8x farther than the arrow at its natural size? Or does the loss in mass somehow counter the increase in speed? Can this elf/halfling duo shoot arrows up to 4800 ft in this way and essentially become a long range sniper?
The Enlarge/Reduce spell states:
The target’s weapons also shrink to match its new size. While these weapons are reduced, the target’s attacks with them deal 1d4 less damage (this can’t reduce the damage below 1).
While this may offer some guidance as to the amount of damage dealt, it does not address this particular situation. I'm looking for answers based in real world physics as well as any D&D based RAW or RAI that may provide some insight.