$5\mathrm{.}16($mod$)$ The 'critical depth' $y$ for a trapezoidal channel carrying water must satisfy the equation

$1-\frac{Q^{2}B}{g{A}^3}=0$

where $Q$ is the flow rate, $B=3+y$ is the channel width, $g=9\mathrm{.}81\frac{m}{s^2}$ is the acceleration due to gravity, and $A=3y+\frac{y^2}{2}$ is the channel cross$-$sectional area. Determine the critical depth $y$ for a flow rate of $Q=20\frac{m^3}{s}$ by writing a user$-$defined MATLAB function that implements the Bisection method as defined below with $x_l=0\mathrm{.}5,x_u=2\mathrm{.}5,{}_s=1\%$ and maximum of $10$ iterations. Carefully note the definition of my func.

Submit printout of function and command window with results.

function $[$xr$,$ fxr$,$ ea$,$ numIter$]=$myBisection$\_$username $($myfunc$,x0,$ es$,$ maxIter$)$

$\%$ Function file: myBisection$\_$username.m

$\frac{8}{8}$

$\%$urpose:

: To determine root of function associated with myfunc using the

B Bisection method

$$

$\%$Record of revisions $($Date $|$ Programmer $|$ Change$)$:

: Date I Name $|$ Original program

$$

$\%$Main Variables:

$\%$INPUTS:

myfunc

function handle for $[fx]=$myfunc$(x)$

$x0-(1x2)$ initial bracket $xL,xU$

$-(11)$ specified error toler

esror tolerance $of5\%$

maxiter $-(1$x$1)$ maximum number of iterations that can be performed

$\frac{2}{0}$

$\%$OUTPUTS :

$xr,-(11)$ estimate of the root

fxr $-(1$x$1)$ value of function at $xr$

ea $-(1$x$1)$ approx. percentage relative error at $xr$

numIter$-(1$x$1)$ number of iterations required to obtain $xr$

$\%$