Physics Forums

## Log in a river

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 $$2\sqrt{2}(Width)$$

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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

Recognitions:      Gold Member        Science  Advisor     Staff Emeritus  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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