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thomblake comments on Harry Potter and the Methods of Rationality discussion thread, part 17, chapter 86 - Less Wrong
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Don't worry, the power drops off with the inverse square of the distance. It's lethal at pretty much any reasonable range, but then drops off quickly after a half mile or so.
I just made that up.
Actually, it spreads as an Airy disc, which gives it a radius of about 300 metres at the far side of the planet, and the effect is divided among all the souls it hits. If you hit a city on the other side of the planet, you just take a couple days off everybody's life. (The technical term is "statistical homicide")
That would make sense as a general rule for spells, otherwise why do they bother having duels face-to-face rather than sniping from nearby mountains? (Or an invisible broomstick 2000m up..)
You do have to aim it by hand and eye. You try hitting a human-sized target from a moving platform at 2km.
Given the descriptions of wandwork we've seen in canon and in MoR so far, I imagine it'd be difficult to reliably hit anything person-sized past thirty feet or so. You can't sight down a wand if you have to swish and flick (though a wizard's staff with a telescopic scope mounted on it is a nice Discworldly image), so it should be about as accurate as throwing a ball -- which is to say not very.
We know of at least one spell that aims itself (Flitwick's) and area affect spells are possible (with a massive fireball it doesn't matter how you aim).
Alternatively, take a potion of +10 accuracy or the equivalent.
Felix Felicis may be the only potion that performs that function, and it's sufficiently broken to be the Potion Not Appearing In This Fic.
Just find something that was made by using up a lot of accuracy. That should do it.
A target with nothing but bulls-eyes will do.