An Interesting Problem July 23, 2009Posted by genericme in Uncategorized.
Though this post isn’t necessarily characteristic of what I’d like to post on in the future, I have an interesting problem that I must share with you all. To encourage everyone to try it, I will not include a solution.
Two points, and , sit on the -axis. Point is at the origin, and point is at . At time , starts moving at a constant speed perpendicular to the -axis, while starts moving with constant speed such that its velocity vector is always pointing in the direction of . Assume . At what time will the points meet?
This problem is much harder than it seems. It comes from a book of physics problems, but I’d really consider it a math problem. I’d like to note that I know of two solutions: an extremely clever solution that requires only a trivial amount of calculus, and a long solution that requires quite a bit of calculus (but that still requires a clever substitution). The latter solution is due to Eric Larson, who solved this problem a few days after I gave it to him. However, I know of no one who has independently thought of the clever solution, and I’ll be extremely impressed if you do! If you’ve seen this problem before, please don’t reveal the solution.