Four bugs are located in the corners of a square, 10 inches on the side. They are arranged like this:

            A---B
            |   |
            D---C 

As the clock starts, A begins crawling directly toward B, which goes to C, C goes to D and D to A.

Each bug will home in exactly on its target, reguardless of the target's motion, so their paths will be curves spiraling toward the center of the square where they will meet.

What distance will each of the bugs have covered by then?

IT WOULD BE INFINATE. THERE WOULD NEVER BE A JOINING PLACE SINCE THEY ARE ALL MOVING TOWARDS THE ONE IN FRONT OF IT. WHICH IS GOING AWAY AT THE SAME CONSTANT RATE, TOWARDS AN ENDLESS, DOWNWARD SPIRRAL. IT MIGHT BE BETTER TO VISUALIZE IT WITH NUMBERS. BECAUSE I KNOW THAT THERE ARE ATLEASED 3 OF YOU THAT NEED HELP ON THIS ONE.. LET'S SAY THAT THE OUTSIDE OF THE BOX IS 0 MINUTES (ZERO) AND THE CENTER POINT IS ONE MINUTE. AND A THRU D IS TRYING TO GET TO ONE THRU UNITS OF TIME AND DISTANCE. SO, LET'S SAY THAT 1/2 WAY IS 30 SECONDS AND 1/2 OF THAT IS 15 SECONDS AND SO FORTH. SO (1/2 + 1/4) = 45 SECONDS. 45 SECONDS + 1/8 (7.5 SECONDS) = 52.5 SECONDS. IF YOU CONTINUE TO ADD UP THE HALFS YOU WOULD NEVER GET TO 1. SO. 1/2 +1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + ...........WILL NEVER EQUAL ONE. YOU CAN ALSO JUST PICTURE IT IN YOUR HEAD UNLESS YOU ENJOY PISSING YOUR LIFE AWAY WITH ANSWERS LIKE THE ONES PREVIOUSLY GIVEN. HOW DO YOU LIKE THEM APPLES?????

Posted by JASON on 2002-05-08 00:02:03