# Cross Section of Irrigation Canal

• Nov 17th 2008, 03:02 PM
Jonboy
Cross Section of Irrigation Canal
A cross-section of an irrigation canal is a parabola. If the surface of the water is 40 feet wide and the canal is 35 feet deep at the center, how deep is it 10 feet from the edge?

I'd show you some work but I'm having trouble visualizing the problem. Any tips on getting me through my haze? Thank you! Love MHF!
• Nov 17th 2008, 03:44 PM
tdschool
• Nov 17th 2008, 06:21 PM
Soroban
Hello, Jonboy!

Quote:

A cross-section of an irrigation canal is a parabola.
If the surface of the water is 40 feet wide and the canal is 35 feet deep at the center,
how deep is it 10 feet from the edge?

I must assume that the canal is full of water.
The cross-section can be graphed like this:
Code:

                |     *- - - - - + - - - - -*(20,35)       ::::::::::|::::::::::       *:::::::::|:::::::::*       *::::::::|::::::::*         *::::::|::::::*             *:::|:::*       - - - - - * - - - - - - -                 |
The equation of this parabola is: . $y \:=\:ax^2$

Since (20,35) is on the curve: . $35 \:=\:a(20^2) \quad\Rightarrow\quad a \:=\:\tfrac{7}{80}$
And the equation is: . $y \:=\:\tfrac{7}{80}x^2$

When $x = 10\!:\;\;y \:=\:\tfrac{7}{80}(10^2) \quad\Rightarrow\quad y \:=\:\tfrac{35}{4}$

And the depth of the water is: . $20 - \tfrac{35}{4} \:=\:\tfrac{45}{4} \:=\:11\tfrac{1}{4}\text{ ft}$

• Nov 17th 2008, 07:24 PM
tdschool
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