Figure $3$: Schematic for curved gate

$4.[17$pts$]$ The massless parabolic gate shown is $W=3m$ wide and pivoted at $O.$ Take $c=0\mathrm{.}15m^{-1},D=2\mathrm{.}5m,$ and $H=9m.$ Determine:

$($a$)7pts$ the magnitude of the vertical force on the gate due to the water mass,

$($b$)8pts$ the magnitude and the line of action of the horizontal force acting on the gate, and

$($c$)2pts$ the horizontal force applied at A required to maintain the gate in equilibrium. Take the line of action for the vertical force to be $\frac{3}{8}\frac{\sqrt[\phantom{2}]{D}}{\sqrt[\phantom{2}]{c}}.$