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.

Clearly,

[1] cos(a) = B/C = B/[100-B] Using the triangle made by the pieces of the pole and the ground

[2] tan(a) = 14.14214/(B-10) Using the triangle made by the upper parts of the pole and the building roof.Iterative solution.

Solve [1] and [2] for B:

[3] B_{1}= 100 cos(a) / [1 + cos(a)]

[4] B_{2}= 10 [ 1 + sqrt(2)/tan(a)]

Evaluate B_{1}and B_{2}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!Direct solution

[5] cos^{2}(x) = 1/[1+tan^{2}(x)]

Square equations [1] and [2] and plug into [5] to get a single cubic equation for B.

[6] -200B^{3}+ 13800B^{2}- 220000B + 1000000 = 0

Equation [6] 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

Started by emeraldcity, Feb 29 2008 04:12 AM

23 replies to this topic

### #21

Posted 05 March 2008 - 01:17 PM

Thank you so much! I have spent a lifetime looking for this answer.Spoiler for Three solutions ...

### #22

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.

### #23

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!

### #24

Posted 07 March 2008 - 09:12 AM

**emeraldcity**,

Kudos for a great puzzle.

- bn

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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