Jena asked:
I’m doing a project in math class on how math relates to archery, and I’m trying to find equations on how to figure the trajectory of an arrow to a target. Just an equation would be wonderful, but pictures would be much more helpful.
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as with any projectile, the trajectory of an arrow can be somewhat predicted using the standard parabolic equations s=vt-1/2at^2 where v is the initial velocity and a is the acceleration caused by gravity. But to get the real trajectory the equation becomes very very complicated. You see an arrow is not a simple projectile, unlike a bullet an arrow has a long shaft, this complicates matters a lot, not only does the shaft increase the area of the arrow causing drag, it also introduces flex. When you shoot an arrow, the front end of the arrow doesn’t accelerate as fast as the tail end, causing the shaft to bend.
There used to be a site written by an engineer, Joe Tapley who is also an archer. His explanation of the physics of arrow flight is the most comprehensive I’ve seen so far. Do a search of his name, there’s bound to be a mirror of it somewhere out there.