The gate $AB$ in Figure below is $0\mathrm{.}8$ m high and $2$ m wide into the paper, hinged at point $A,$ and restrained by a stop at $B.$ Assume the density of the water to be $1000k\frac{g}{m}3.$ If the water depth is $2\mathrm{.}1$ m $,$ compute $(20\text{'})$

$(1)$ The average pressure on the gate.

$(2)$ The hydrostatic force acting on the gate.

$(3)$ The location of the center of the pressure.

$(4)$ The horizontal force at point B$.$