Exercise $4$

The rectangular gate, $5$ m wide and $200$ kg $,$ illustrated in Figure $4$ is hinged at $\backslash ($ B $\backslash )$ and rests against the ground at $\backslash ($ A $\backslash ),$ forming a $\backslash (45^\{\backslash$circ$\}\backslash )$ angle with the horizontal.

The gate must be opened from its lower edge by applying a normal force at its center. Determine the minimum force $\backslash ($ F $\backslash )$ required to open the water gate.