Consider a detention basin designed to capture excess flood waters that is trapezoidal in shape,

with surface area as a function of depth given by:

$A(h)=20+10h$

and the outflow from the basin is a function of the depth:

$Q_{\text{o}\text{u}\text{t}}=\sqrt[\phantom{2}]{19\mathrm{.}6h}$

If a rainfall event produces inflow to the basin at a constant rate of $10\frac{m^3}{s}($and it goes on for a

very long time$)$:

a$.$ Determine the maximum depth that is reached in the basin

b$.$ Determine the surface area of the basin at that depth

c$.$ Write a differential equation to describe how the depth varies in time $($i$.$e$.,$ what

equation would you need to solve to determine $h(t)?)$