Question

A drainage canal has a cross section in the shape of a parabola. Suppose that the canal is 10 feet deep and 20 feet wide at the top. If the water depth in the ditch is 5 feet, how wide is the surface of the water in the ditch?

Answer 1

Answer:

The answer is "$\bold{10\sqrt{2}}$".

Step-by-step explanation:

Equation of the parabola:

$\to y=ax^2 \ \ \ \ \ \ \ \ \ _{where}, (x,y) _{are} (10,10)$

$\to 10=a(10)^2\\\\\to 10=100a\\\\\to a=\frac{10}{100}\\\\\to a= \frac{1}{10}$

if the value of a= $\frac{1}{10}$ then put the value into the equation:

$\to y=\frac{x^2}{10}$

when depth of water y=5

$\to 5=\frac{x^2}{10}\\\\\to x^2=50\\\\\to x=\pm\sqrt{50}$

So, width:

$\to 2\sqrt{50}=2\sqrt{25 \times 2}$

             $=2 \sqrt{5^2\times 2}\\\\=2\times 5 \sqrt{2}\\\\=10\sqrt{2}$