(Solved): A gate having a triangular shape shown in the figure below is located on the vertical side of an o ...

A gate having a triangular shape shown in the figure below is located on the vertical side of an open water tank. The dimensions and the suggested coordinate system (in red) are shown in the figure. Some related relations for the triangular shape are also given below. The density of the water is $$1000\mathrm{kg}/{\mathrm{m}}^3$$ $$\begin{array}{l}{T}_x\hat{x}=\frac{w{L}^3}{36}\\ I_x\hat{y}=0\end{array}$$ The centroid of the gate under the given coordinate system in the figure, in meter, is: $$y=37,x=1$$ $$y=2,x=2$$ $$\begin{array}{l}y=12,x=0\\ y=65,x=0\end{array}$$ Question 11 The net resultant force of the water acting on the gate is about: $$28953.1\mathrm{kN}$$ The point of application of the resultant force in meter, which is measured from the liquid free surface, is: $$x=0,y=15.47$$ $$x=0,y=3.85$$ $$x=0,y=12.17$$ $$x=0,y=6.50$$ Question 13 5 pts If the gate is hinged at the top $$(y=8\mathrm{m}$$ in the figure), the normal force applied at the bottom $$(y=14$$ $$\mathrm{m}$$ in the figure) to keep the gate closed, in $$\mathrm{kN}$$, is: about $$231.0$$ about $$1473.0$$ about $$17843.0$$ about $$675.0$$