(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rectangular swimming pool is 20 feet wide and 40 feet long. The depth of the water varie uniformly from 3 feet at one end to 9 feet at the other end. Find the total force exerted at the bottom of the pool.

2. Relevant equations

The force F exerted by a liquid of constant density "p", where the functions f and g are continuous on [c,d], is

\begin{equation}

F=\int_c^d \, p(k-y)[f(y)-g(y)]dy

\end{equation}

The equation of the line making up the bottom of the pool is

\begin{equation}

\frac{-3}{10}x+6=y

\end{equation}

3. The attempt at a solution

The depth of any rectangle below the surface would be (9-y), I reasoned.

I tried to do the integration

\begin{equation}

\begin{split}

F&=62.5\int_0^6 (9-y)(\frac{10(y-6)}{-3})dy\\

&=26250\\

\end{split}

\end{equation}

The book says this answer is wrong, as I suspected. I can't seem to find a way to think of it. Ways I've tried:

Finding the volume of water above the wedge caused by the incline + the wedge volume * 62.5

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# Homework Help: Force Exerted By a liquid integration problem

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