$2\mathrm{.}109$ Water backs up behind a concrete dam as shown in Fig. $2\mathrm{.}109.$ Leakage under the foundation gives a pressure distribution under the dam as indicated. If the water depth, $h,$ is too great, the dam will topple over about its toe $($point $A).$ For the dimensions given, determine the maximum water depth for the following widths of the dam, $l=20,30,40,50,$ and $60ft.$ Base your analysis on a unit length of the dam. The specific weight of the concrete is $150l\frac{b}{f}{t}^3$