$($the program used for these questions is matlab$)$

Question $1[9$ points$]$:

The force exerted during a jumping motion $(F,[lb])$ depends on the mass of the person jumping $(m[$lb$])$ and the "lift$-$off"

time $([ms])$ spent pushing the body upwards off the floor from a stationary position, starting at time $t=0.$

$F(t)=3$msin$(\frac{}{}t)+m(1-\frac{t}{})$

For a person with a mass of $189$ lb $,$ jumping with a lift$-$off time of $135$ ms $,$ we want to determine the time at which the

force exerted is equal to $615$ lb $.$

a$)$ Plot the function in the form $f(x)=0$ from $t=0-80ms.[2$ points$]$

b$)$ Starting with an estimated solution of $30$ ms and approximate relative error $({}_a)$ of $100\%,$ calculate and report

solutions using the Newton$-$Raphson method until ${}_a$ falls below $0\mathrm{.}1\%.("$Report solutions" means make these values

show up in your published solution$).[2$ points$]$

c$)$ Add red circles on top of your curve from $($a$)$ showing the estimated solutions from $($b$)($including the starting

estimate$).[1$ point$]$

d$)$ Plot the approximate relative error at each iteration of the Newton$-$Raphson method and report the final value. $[2$

points$]$

e$)$ Use Matlab's built$-$in function to estimate the solution. Report this value and add the solution as a circle to your plot

from part $($b$).$ Use a different color from your circles added in $($c$)[2$ points$]$