Problem $2$: There is a semicircular plate in the schematic blow. Width is $3$ m long $($into the page$)$ and it act as a gate in a reservoir. Determine the resultant force the water pressure exert on the plate and then find the force on the hinge B and point A $.$ Note that there is no friction at A $.$ Neglect the weight of the plate.

The centroid of the semicircular area is shown in the schematic.

$(20$ points out of $60$ points$)$