The flow of water from a reservoir is controlled by an $2m$ width and $6m$ height rectangular gate hinged at point A and slanted at angle theta, as shown in the figure. The gate is kept closed by putting a mass, $M$ at the end of a horizontal arm, $3m$ from the hinge. The weight of the gate and the friction at the hinge are negligible. If it is desired that the gate be opened when the height of the water is $4m,$ determine the mass, M$,$ when the gate is about to open. The slanted angle of the gate is such that Sin theta $=0\mathrm{.}8.$ Use density of water of $1000k\frac{g}{m^{{?}^{{?}^{?}}}}3,$ and gravity of $9\mathrm{.}81\frac{m}{s^{{?}^{{?}^{?}}}}2$