Answer
$6533.33 \ N $
Work Step by Step
The width of the dam at height $y$ is given by $-y=-2x \implies y=2x \implies x=0.5 y$
So, $w(y)=(2)(0.5)y=y$
We need to use the formula such as: $F=\int_b^t \rho g (a-y) w(y) \ dy$.
Plug in the above formula the given values to obtain:
$F=\int_b^t \rho g (a-y) w(y) \ dy \\= \int_0^{1} \rho g (2-y) y \ dy\\=\dfrac{2}{3} \times \rho g \\=(\dfrac{2}{3}) (1000) (9.81) \\=6533.33 \ N $
