Remaining Time: $04$:$36$:$31$

A vertical dam has the form of an isosceles trapezoid with horizontal sides parallel. The dam is $30$ m high, $40$ m in its lower part and $60$ m in its upper part. Finally, the dam retains $25$ m of water, as indicated in the figure below.

a$)$ Let $y$ denote the height in meters measured from the base of the dam. The hydrostatic force exerted by the water on the portion of the dam comprised between $ym$ and $y+ym$ is approximately $p(y)yN.$ What is $p(y)?$ Note that the density of water is $=1000K\frac{g}{m^3}$ and the acceleration due to gravity on the earth's surface is $q=9\mathrm{.}8\frac{m}{s^2}.$ Express your answer as a formula.

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b$)$ In Newtons, what is the total hydrostatic force exerted on the dam?

FORMATTING: If you round your answer, ensure that the round$-$off error is less than $1\%$ of the value.

Answer