An impossible game of catch?

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.

4 thoughts on “An impossible game of catch?

  1. 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.

  2. 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

  3. 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.

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