Log Length in L-shaped River Channel

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SUMMARY

The discussion focuses on calculating the longest possible log that can float in an L-shaped river channel formed by two rivers of widths 64m and 125m. The solution involves deriving a formula for the length of a line that passes through the inner corner of the channel. A recursive algorithm was initially attempted but faced challenges when the log length reached 2√2 times the width. The optimal approach includes drawing a diagram and using calculus techniques, specifically finding the minimum length through derivative analysis.

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  • Understanding of basic geometry and properties of right angles
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  • Experience with recursive algorithms in programming
  • Knowledge of optimization techniques in mathematical problems
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Homework Statement



Two rivers of unequal width (64m and 125m) meet at a right angle, forming an L-shaped channel. What is the longest possible log you can float on it?

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The Attempt at a Solution


I tried for equal widths and built a recursive algorithm for turning the log. But it is getting stuck if the log is [tex]2\sqrt{2}(Width)[/tex]
 
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the log will turn around the inner corner. just find a formula for finding the length of a line entirely in the water which passes through that point. then find the minimum
 
Start by drawing a picture. Draw two channels of width 64 and 125 and draw a straight line from the outside edges just touching the inside corner. You should be able to find a formula for the length of that line in terms of x, the distance from the outside corner to one of the ends of the line. Then find x which minimizes length. You MIGHT be able to get that by completing the square but I seem to remember a problem like this requiring a derivative. Are you sure this is "precalculus"?
 

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