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Log in a river

by GPhab
Tags: river
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Oct9-08, 08:28 AM
P: 25
1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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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Oct9-08, 09:04 AM
P: 2,258
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
Oct10-08, 02:54 PM
Sci Advisor
PF Gold
P: 39,345
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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