Gates in the Poe Lock at Sault Ste. Marie, Michigan, close a channel \(W=34 \mathrm{~m}\) wide, \(L=360 \mathrm{~m}\) long, and \(D=10 \mathrm{~m}\) deep. The geometry of one pair of gates is shown; each gate is hinged at the channel wall. When closed, the gate edges are forced together at the center of the channel by water pressure. Evaluate the force exerted by the water on gate \(A\). Determine the magnitude and direction of the force components exerted by the gate on the hinge. Neglect the weight of the gate.

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Plan view: Water Hinge Gate A 15 P3.47 W = 34 m