Thank you so much! I have spent a lifetime looking for this answer.Spoiler for Three solutions ...Let B be the height of the break and C the part that fell. B+C = 100 ft.
Consider the angle the two parts of the flagpole make where it breaks.
Call that angle a.
 cos(a) = B/C = B/[100-B] Using the triangle made by the pieces of the pole and the ground
 tan(a) = 14.14214/(B-10) Using the triangle made by the upper parts of the pole and the building roof.
Solve  and  for B:
 B1 = 100 cos(a) / [1 + cos(a)]
 B2 = 10 [ 1 + sqrt(2)/tan(a)]
Evaluate B1 and B2 for various values of a. Solution is when they are equal.
Three solutions are found.
B1 = 48.4116 ft - for - a1 = 20.2123 deg
B2 = 11.9343 ft - for - a2 = 82.2115 deg
B3 = 8.65411 ft - for - a3 = -84.56367 deg - For this solution, the flagpole fell in the opposite direction!
 cos2(x) = 1/[1+tan2(x)]
Square equations  and  and plug into  to get a single cubic equation for B.
 -200B3 + 13800B2 - 220000B + 1000000 = 0
Equation  has the same three solutions.
Check them here:
B1 = 48.411547 ft
B2 = 11.93433 ft
B3 = 8.654118 ft
B1 solution is shown in black.
B2 solution is red.
B3 was not drawn. It would have gone from the upper right corner of the building back to the left.
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Guest Message by DevFuse
23 replies to this topic
Posted 05 March 2008 - 01:17 PM
Thank you so much! I have spent a lifetime looking for this answer.Spoiler for Three solutions ...
Posted 07 March 2008 - 04:56 AM
It is, indeed, at the corner. I apologize for not being clear in stating the situation.
Judging from the discussion in the first few posts, the flagpole is on one corner of the building.
It then falls diagonally toward the building so that the broken part passed directly above the center of the roof.
Posted 07 March 2008 - 05:03 AM
Once again, I feel the need to apologize for not being clear in stating the situation. It was not deliberate. I had such a clear picture in my mind after this haunting me for so long, that I failed to clearly relay accurately the problem as presented to me as a child.
Structural integrity failed at a point:
1a - time of failure (compromised structual integrity)
1b - time untill faliure occured - in situ.
2 - How did it become weak? (least strength - if wooden then, at lowest density, natural defects, manufacturing defect, decay, infestation, felling defects etc. - if metal then, rust, poor manufacture, weak weld etc)
3 - where along the section/axis did failure occur
Most people will answer for No. 3 probably due to the information available.
The others are not excluded other than by lack of information.
Is this a deliberate attempt to get people to respond, request more information?
Is it a flawed puzzle?Spoiler for Sorry for waffle!
Posted 07 March 2008 - 09:12 AM
Kudos for a great puzzle.
Kudos for a great puzzle.
Vidi vici veni.
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