Continuing on the original problem here, posted by Jer.

During a gale a maypole was broken in such a manner that it struck the ground at a distance twenty feet from the base of the pole.

It was repaired without any gain or loss in its length. Later it broke a second time at a point below the earlier by an amount exactly equal to the difference in length of the two sections of the first break.

How far did it strike this time from the base?

Let L be the length of the pole and x the height
of the first break, then

   (L - x)^2 = x^2 + 20^2

             or
  
   L*(L - 2*x) = 20^2

The difference in length of the two segments is
L - 2*x. If z is the distance from the base on the
second break, then

   z^2 = [(L - x) + (L - 2*x)]^2 - [x - (L - 2*x)]^2

       = 3*L*(L - 2*x)

       = 3*20^2

Therefore,

   z = 20*sqrt(3) feet.
  

Posted by Bractals on 2006-06-12 10:33:51