$1-(15)$ A gate, in the shape of a quarter$-$cylinder, hinged at A and sealed at $C,$ is $w=2m$ wide. The bottom of the gate is $H=4m$ below the water surface. $R=2m$; ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=9800\frac{N}{m^3}$

$($a$)(5)$ First express and then calculate the horizontal force acting on the surface $AB,$

$($b$)(5)$ First express and calculate the line of action of this force and show it on the figure, $($c$)(5)$ First express and then calculate the vertical force acting on the surface $AB.$