$.$ As shown in the notes, the velocity as a function of time $($t$)$ for a object of mass m

falling due to gravity $($g$)$ and subject to aerodynamic drag $($drag coefficient cd$)$ is given

by

v$($t$)=$ rgm

cd

tanh r

gcd

m

t

where tanh is the hyperbolic tangent. From an experiment for an object with mass

m $=74$ kg$,$ a velocity of $40$ m$/$s is measured after $5\mathrm{.}5$ s of free fall. Given this data,

it is possible to determine the drag coefficient by solving the nonlinear equation above

for the given data and with g $=9\mathrm{.}81$ m$/$s$2$

$.$

For this problem, you will determine the value of cd for the given data using the

bisection method by hand calculation. You can use your calculator $($if it has the tanh$)$

or a MATLAB anonymous function to calculate the values of f$($cd$).$ First, put the

nonlinear function in the form f$($cd$)=0.$ Start with an initial bracket for cd between

$0\mathrm{.}2$ and $0\mathrm{.}3.$ Create a table similar to Table $1$ of Chapter $03\mathrm{.}03$ in the HNM text.

Iterate until the approximate relative error falls below $0\mathrm{.}01\%.$ If you use MATLAB,

show the form of the anonymous function $($you can write it on paper, you don$$t need

the output from MATLAB$).$ The relati