You have a rectangular door that is $1$ meter wide and $1\mathrm{.}5$ meters high, mounted on hinges in a vertical wall of a water tank. The door is hinged along its upper edge and is subjected to water pressure due to the water stored in the tank. The water exerts a hydrostatic force on the door, and atmospheric pressure acts on the outside surface of the door. The door is located at a depth of $2$ meters below the surface of the water.

$($a$)$ Find the total hydrostatic force exerted on the door due to the water pressure $(7$ pts$).$

$($b$)$ Find the line of action of the resultant hydrostatic force exerted on the door $(7$ pts$).$

$($c$)$ Find the force $(F_B)$ that must be applied at the bottom edge of the door to keep it closed $(7$ pts$).$

$($d$)$ Determine the force exerted at the hinge $(F_A)(7pts).$

$($e$)$ Does the ratio of $\frac{F_B}{F_A}$ have a maximum by varying L$?$ If so$,$ what's the maximum ratio? $(7$ pts$)$

$($f$)$ Bonus: Sketch the variation of the $\frac{F_B}{F_A}$ versus $\frac{H}{L}(5$ pts $).$