Ammunition speed is not based within the rules of the game we're discussing. I suggest no check and not burying the players under a mountain of checks for something as basic as seeing where a magically enchanted arrow/bolt goes for a spell that already requires a dex saving throw to do barely any damage. Less is more in this kind of situation.
You have to consider what is trying to be achieved here and how it is being achieved. Mechanics aside, my perspective is from a storytelling perspective and considered general physics.
You have an arrow stuck in the ground that quickly flies to a target and vanishes. The target is invisible, and taking damage doesn't change that. The information that would be easily available is what direction the arrow moved, but the actual location that the arrow vanished would not be that easy to find. There is a chance that the player would see it, but there is a higher chance they would not.
I argue this considering reality. If I fire an arrow at a target that arrow is easily visible when it leaves my bow, but depending on how well my ability to perceive it is, and the strength which the bow is drawn determines how well I see it as it moves through the air. Add to that a component where the arrow vanishes upon impact to the target and suddenly the opportunity to miss that event increases. In the hands of a skilled archer the average arrow from a longbow moves at the rate of 190fps (~129mph. The human eye can see at the frame rate of 10-12. I have seen videos of an arrow fired from a longbow in slow motion that were shot at a frame rate of 5000 and the arrow travels 30ft in less than a second. An object moving at just 20 mph moves 30ft in one second so you are talking more than 6 times that fast.
The spells states: "
whenever a creature other than you comes within 30 feet of the ammunition for the first time on a turn or ends its turn there, one piece of ammunition flies up to strike it." That means that the PC has 100ths of seconds to see the arrow move and determine where the location is vanished at. It is nearly impossible for the human eye to catch a motion that quickly. We are talking about motion that the character might not be able to see, then the object they are attempting to track vanishes instantly. You have to ask how could the character see that. There is a chance but no matter how you slice it a Perception Check is required.
Applying a check to actually catch the spot that the arrow vanishes isn't creating a mountain of checks. Its one, and that simply gives the players a chance to notice that location. A single check isn't going to bog down the game, unless you follow it with a ton more checks related to it.
I am reading
Of Dice and Men by David Ewalt and in Chapter 2 or 3, his character, Weslocke, enounters a similar situation. In that case the character used
Summon Monster VI to summon yeth hounds to track the invisible creatures. Achieving a similar objective, but with objects that do not disappear. Once they saw where the yeth hounds were attacking the party moved closed in on the creatures to beat them.
If I were the DM in this case, I would tell the player the direction the arrow moved, but require a Perception check to locate the exact location simply because without magical improvements, no PC could actually see an object moving at 190fps that vanishes the instant of impact.
