As anyone who's ever heard the story of William Tell can attest, shooting an object with extreme precision, especially something like an apple off of someone's head, with a bow and arrow takes a ton of skill, practice, and luck. It gets even crazier when you see somebody shoot an object the size of a dime flying through the air. Just how do stunt archers do this?
First of all, its nowhere near as easy as "train until you are 100% accurate," as arrows don't fly straight. What's that? Years of high school archery in gym proves otherwise? Well, first of all, congratulations on actually being able to aim, and second of all, you're only examining the arrow's flight path as a whole. Yes, the arrow's center of mass does behave like a simple projectile, so, for larger targets, its fine. However, as the arrow flies, the shaft of the arrow actually bends back and forth in a motion resembling a wave. This motion actually is what enables the arrow as a whole to fly in a straight line, as it otherwise would simply fall flat on the ground. As such, stunt archers need to be able to figure out where the arrowhead will be when the arrow travels to its target. This, believe it or not, can actually be brought down to a science. Simply by knowing the strength of the material that the arrow is made of, as well as the distance between the arrow and the target, archers can accurately predict if the arrowhead will actually be in the right position to hit the target. As such, most stunt archers actually use a device to measure the strength of said arrow, and will only shoot with arrows falling within a very specific range.