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The parabolic gate shown is {a} m wide ; $c$ = {c}$ m^{-1}$, $H$ = {H} m.

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Consider the $\\rho_{\\text{Water}}$ = 1000 $kg/m^3$ and $g$=9.81 $m/s^2$. 

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$\\textbf{(a)}$ Determine the magnitude of the vertical force acting on the gate

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$\\textbf{(b)}$ Determine the line of action for the force in part a

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$\\textbf{(c)}$ Determine the magnitude of the horizontal force acting on the gate

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$\\textbf{(d)}$ Determine the line of action for the force in part c (from where y= 0)

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$F_{\\text{V}}$= [[0]] kN

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$x\\prime$ = [[0]]  m

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$F_{\\text{H}}$ = [[0]] kN

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$y\\prime$ = [[0]] m.

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