*Tristan and his friend Joe are playing a game of catch. They are fifty feet apart from each other and tossing the ball back and forth at approximately seventy-five feet per second. Two thirds of a second elapse between each of the throws of the ball and the corresponding catch. During that time the ball travels one hundred and sixty seven feet. How is this possible?*

Ok, so my first attempt at a lateral thinking problem was a bit of a disaster. Konrad and Jason both were not happy with it and I am trying to figure out a way to re-work it so that the problem is not trying to figure out what the heck I am thinking!

Apparently since I want to publish I need to hold off on posting answers here for copy write reasons. So I will post the answers on a separate site and use comments here as a way to discuss the problems.

So Jason just pointed out to me a solution I had not considered. The two guys could be standing 50 feet apart and bouncing the ball off of a wall – so the resulting part of the path is some arbitrary length.

I don’t think the problem as I phrased it is solved by this solution though since it has the same hook as my initial problem – namely that the ball is thrown at 50 feet per- second, travels for one third of a second, and yet travels five times farther than we would expect.

They play catch inside a train that’s traveling 175.5 ft/sec

not quite … I was not considering that no matter which direction the ball is thrown it travels 167 ft … well if thrown perpendicular to the trains travel that actually works.

The train is actually going 240 ft/sec and the ball is being thrown perpendicular to the trains direction of travel. The ball flies 50 feet perpendicular and 2/3*240ft = 160 ft in the direction of travel. The total travel is sqrt(50*50+160×160) = 167.631ft

Ok, so dont look at the answer I just sent you. I just saw your second comment. Perpendicular to the trains motion? Do you mean parallel to?

I had not considered this but having the two people on different trains that were traveling parallel to each-other and at the same speed. Is that what you mean? In that case they really could be throwing the ball perpendicular to the trains motion.

Either way – I think I may like the train problem better than my solution. Especially since with talking to you about guys throwing balls on a train lets me use the word gedankenexperiment, both a cool word *and* has the benefit that if you imagine me saying it at all you are sure to get annoyed at how I am butchering your native tung. Always fun.