Log Length in L-shaped River Channel

  • Thread starter Thread starter GPhab
  • Start date Start date
  • Tags Tags
    Log River
AI Thread Summary
The discussion centers on determining the longest log that can float in an L-shaped river channel formed by two rivers of widths 64m and 125m. A recursive algorithm was initially attempted for equal widths, but complications arose when the log reached a specific length, causing it to turn at the inner corner. The solution involves drawing a diagram of the channels and deriving a formula for the length of a line that touches the inner corner. The goal is to minimize this length by finding the optimal distance from the outer corner to one end of the log. The complexity of the problem suggests it may require calculus techniques rather than just precalculus methods.
GPhab
Messages
24
Reaction score
0

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?

Homework Equations





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)
 
Physics news on Phys.org
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"?
 

Similar threads

I Where Should the Bridges be Built to Minimize Road Length?
Replies
4
Views
2K
Calculating the Planck Length
Replies
3
Views
203
The problemFind side length using trig
Replies
6
Views
3K
I Compute Length Contraction: Is ##l=1## a Possible Model?
Replies
33
Views
2K
Tension in a deformed cylindrical bag on a surface
Replies
18
Views
1K
What Minimum Speed Must Jane Have to Swing Across the River?
Replies
1
Views
2K
How Can Vernie and George Swing Across the River Despite the Wind?
Replies
1
Views
4K
To find the centre of gravity of a lamina
Replies
2
Views
2K
Surface roughness in 2D sinusoidal corrugation
Replies
1
Views
4K
What is the best shape for a soccer goal post?
4
Replies
157
Views
11K

Hot Threads

Recent Insights

Back
Top