How can Robin Hood save Maid Marian?

Question

This is just for fun. Don't try to solve it, just explain how you'd set up the problem.

At King John's summer games, the Sheriff of Nottingham, Maid Marian, and Robin Hood are all far apart in a triangle. The sheriff accidentally lofts an arrow that will land on Maid Marian, but a short time later with quick reflexes, Robin carefully takes aim and launches an arrow that deflects the sheriff's projectile, thus saving the Maid's life.

How would you set it up?

Oh -- since the sheriff was just playing around, he shot his arrow with a high trajectory up into the air; it would've hit the maid on the way back down. Robin, on the other hand, purposefully shot with a low trajectory and high velocity. Due to the delay caused by reflex time, the arrows collided when the sheriff's arrow was on its downward path, while Robin's arrow was still climbing.

Hope that helps.

Answer 1

This seems like an intersection of two parabolas to me. For starters, I don't care that they're in a triangle, I just care that the arrows hit each other. So I might as well assume that Robin shot his arrow in the same vertical plane that the sheriff did. I'd do a time v. height graph, and draw two reasonable parabolas.

Answer 2

You could have a rather large triangle, and have a figure representing maid marian, and something that would represent the arrows that robin hood and the sheriff would be shooting off. you would need a machine that could accurately hit off the representation of the arrows of robin hood and the sheriff. you would need something that would also calculate the speed needed for a representation to hit the other one from the distances that they are from.