Originally posted by talzamir
A hunter is trying to kill a monkey by using a bow and arrow. His arrow has an initial velocity of v in a direction of his choice, and the monkey is up a tree at some point (a,b) relative to the hunter's location (0,0), where a and b are both > 0. At the very instant that the arrow is launched the monkey lets go of the branch and tries to avoid the arrow by dropping to the undergrowth and then running away.
How should the hunter aim the arrow?
The hunter should make sure to stand (almost) directly below the monkey, and aim straight up. That way, the monkey can drop all he likes. In mathematical terms, the hunter should ensure that |b| < size of monkey's backside/2.
You may call that cheating the problem, and you'd be right, of course. But if you watch documentaries, you'll see that this is often the method employed by real rainforest hunters with blowpipes: don't fire sideways, fire up. It reduces the margin of error.