Answer:
[tex]F=4673.95lbs[/tex]
Explanation:
Recall weight density of water 62.5 lb/ft^3 and the height 6ft base 8ft
The width of the triangle
[tex]\frac{W(x)}{7}=\frac{(8-x)}{2}[/tex]
The hydrostatic force is the pressure times area of the submerged
[tex]W(x)=\frac{7*(8-x)}{4}[/tex]
[tex]F=\int\limits {p} \, dA[/tex]
[tex]F=\int\limits^8_2 {pgx*\frac{7}{4}*(8-x)} \, dx[/tex]
[tex]F=\int\limits^8_2 {62.5*\frac{7}{4}*x*(8-x)} \, dx[/tex]
[tex]F=109.375\int\limits^8_4{(8x-x^2)} \, dx[/tex]
[tex]F=109.375[4x^2-\frac{1}{3}x^3]|4,8[/tex]
[tex]F=109.375*42.73=4673.95lbs[/tex]
