The uniform rectangular relief gate $AB$ has a weight of $800$ lb and a

width of $2$ ft $.$ Answer the following questions $[16$ points$]$:

a$.$ Draw the load distribution due to the force exerted by water on

the gate $AB.$

b$.$ Determine the net resultant force exerted by water on the gate

$AB$ and the location of this force along the surface measured

from $B.$

c$.$ Determine the normal reaction at the smooth support $A.$

d$.[$Optional Extra Credit, $4$ points$]$ Determine the components

of reaction at the pin $B.$