The container shown below contains water $)$ and extends $c=5m$ into the page. The top of the container is sealed shut by a massless gate angled at $=45$ to the horizontal. The water level in the container is $b=1\mathrm{.}5m$ above the hinge, as shown. Above the water in the container there is air at a pressure of $2$atm $($absolute$).$ The air outside the container is at $1$atm absolute pressure. The apex of the container is $a=1m$ above the water surface. Determine the force, $F,$ that must be applied perpendicular to the gate at the location shown to hold the gate shut.