Water $(=1000k\frac{g}{m^3})$ is contained behind a semi$-$circular gate, $AB$ with a radius of $R=2\mathrm{.}0m$

and width into the page is $5$ m $.$ The gate is hinged at point A$.$Neglect the weight of the gate.

Calculate:

a$)$ The resultant hydrostatic force applied on gate $($AB$).$

b$)$ The center of pressure on the gate

c$)$ The minimum horizontal force $(F_B)$ at point B needed to hold the gate in place