Problem $1(25$ Pts$)$

Suppose that a rectangular tank, partly filled with liquid and open to the atmosphere, is subjected to a constant horizontal acceleration of $\backslash (2\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ),$ as shown in the below figure. The width of the tank is $8$ m $.$ Determine the level of the gas$-$liquid interface in the moving tank, $\backslash ($ h$($x$)\backslash ),$ given that the level at rest is $\backslash ($ h$\_\{0\}=3\backslash$mathrm$\{$~m$\}\backslash ).$ Also, calculate the maximum height of the gas$-$liquid interface in the moving tank. Assume that the gravity acceleration is $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ),$ the variations in the $\backslash ($ y $\backslash )-$direction are neglected, and the center of the tank bottom is the point of the origin.