Problem $1(20$ points$)$

Create a function to find roots using Bisection method. The function should take maximum

iterations and maximum error as input arguments. The function should check if maximum

iteration and maximum error is given as input arguments while calling the function. If not

defaults value of desired relative error should be $0\mathrm{.}00001\%$ and default value of maximum

iterations should be $50.$ The function should quit if either the relative error is less than the desired

relative error or iterations are greater than or equal to maximum iterations.

Use this function to determine the mass of the bungee jumper with a drag coefficient of $0\mathrm{.}25$

$k\frac{g}{m}$ to have a velocity of $36\frac{m}{s}$ after $4$ s of free fall. Note $g=9\mathrm{.}81\frac{m}{s^2}$

The function to be evaluated is

$f(m)=\sqrt[\phantom{2}]{\frac{gm}{c_d}}tanh(\sqrt[\phantom{2}]{\frac{g{c}_d}{m}}t)-v(t)$

in MATLAB