$\%$Red Bull Data plotted.

close all

clear

$\%$ Read data from file

$\%$ First column is time in secs

$\%$ Second column is velocity

$\%$ Third column is theoretical terminal velocity at that time

jumpdata $=$ csvread$(\text{'}$RedBullJumpData$.$csv$\text{'})$;

t$\_$redbull $=$ jumpdata$($:$,1)$;

v$\_$redbull $=$ jumpdata$($:$,2)$;

terminal$\_$velocity $=$ jumpdata$($:$,3)$; $\%$ You need to use this in the last question

N$\_$timestamps $=$ length$($t$\_$redbull$)$;

$\%$Calculate freefall velocity vector here

g $=9\mathrm{.}81$;

v$\_$freefall $=$ g $*$ t$\_$redbull;

$\%$rand$($size$($t$\_$redbull$))*20+100$;

$\%$ Part $1$

$\%$ We are giving you this answer for free

figure$(1)$;

h$\_$part$1=$ plot$($t$\_$redbull, v$\_$redbull, $\text{'}$r$-$x$\text{'},$ 'linewidth', $2\mathrm{.}0)$;

shg;

hold on;

$\%$ Part $2$

$\%$ This plot does not have the right linewidth. You fix it$.$

h$\_$part$2=$ plot$($t$\_$redbull, v$\_$freefall, $\text{'}$b$--\text{'})$;

shg;

$\%$ This is how to put on a grid

grid on;

$\%$ This is how to fix an axis to a desired size

$\%$ axis$([$something goes in here$])$;

axis$([01800400])$;

$\%$ Set the fontsize and label the graph here!!

$\%$ Calculate when he hits the atmosphere

$\%$ Part $3$

$\%$ Need some stuff here $...$ or read it off from the graph

v$\_$err $=$ v$\_$redbull $-$ v$\_$freefall;

hit$\_$instant $=75$; $\%$ This is wrong

fprintf$(\text{'}$Mr$.$ B hits the earth'$\text{'}$s atmoshpere at $\%$f secs after he jumps

$\text{'},...$

hit$\_$instant$)$;

$\%$ Part $4$

$\%$ Now starting from the velocity and time $=56$ secs

$\%..$ let's update and calculate v

g $=9\mathrm{.}81$;

v$\_$numerical$\_1=$ zeros$(1,$ N$\_$timestamps$)$;

drag$\_$constant $=3/60$;

start $=$ find$($t$\_$redbull $==56)$;

$\%$ Starting from this time instant, calculate the velocity required

v$\_$numerical$\_1=$ v$\_$redbull $-20$; $\%$ This is wrong $..$ for you to fix

$\%$ Plot using the dashed green line with $(+)$ markers

h$\_$part$4=$ plot$($t$\_$redbull, v$\_$numerical$\_1,\text{'}$g$+--\text{'},$'linewidth',$2\mathrm{.}0)$;shg

$\%$ Part $5$

$\%$ Calculate the percentage error as required

per$\_$error $=$ rand$(1,2)$; $\%$ This is just some random number $..$ which is wrong

fprintf$(\text{'}$The percentage error at $69$ and $180$ secs is $\%1\mathrm{.}1$f and

$\text{'},$ per$\_$error$(1))$;

fprintf$(\text{'}\%3\mathrm{.}1$f respectively

$\text{'},$ per$\_$error$(2))$;

$\%$ Part $6$

$\%$ You'll need to modify your euler loop here to do heun instead

$\%$ Also update the drag constant at every timestamp and change the update

$\%$ calculation to allow for the new v$^2($t$)$ term

$\%$ A hint here that now you have to calculate the velocity using the new

$\%$ differental equation

$\%$ constant $..$ put it in v$\_$numerical$\_2$

v$\_$numerical$\_2=$ rand$($size$($t$\_$redbull$(21$:end$)))*50+200$;

$\%$ This is the handle plot for part $6.$ You have to plot the right stuff not

$\%$ this stuff.

$\%$ Note that the plot linewidth and colour are wrong. Fix it$.$

h$\_$part$6=$ plot$($t$\_$redbull$(21$:end$),$ v$\_$numerical$\_2,\text{'}$c$--\text{'})$;

shg

est$\_$error $=9\mathrm{.}0$;

fprintf$(\text{'}$The error at t $=100$ secs using my estimated drag information is $\%$f

$\text{'},$ est$\_$error$)$;

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%$ DO NOT EDIT BELOW THIS LINE THIS IS TO MAKE SURE YOU HAVE USED THE

$\%$ VARIABLES THAT WE ASKED FOR

$\%$ Check for existence of variables

if $($~exist$(\text{'}$v$\_$freefall', 'var'$))$

error$(\text{'}$The variable v$\_$freefall does not exist.$\text{'})$

end;

if $($~exist$(\text{'}$hit$\_$instant', 'var'$))$

error$(\text{'}$The variable hit$\_$instant does not exist.$\text{'})$

end;

if $($~exist$(\text{'}$per$\_$error', 'var'$))$

error$(\text{'}$The variable per$\_$error does not exist.$\text{'})$

end;

if $($exist$(\text{'}$per$\_$error', 'var'$))$

l $=$ size$($per$\_$error$)$;

if $($ sum$($l $-[12])$ ~$=0)$

error$(\text{'}$per$\_$error is not a $2$ element vector. Please make it so$.\text{'})$

end;

end;

if $($~exist$(\text{'}$v$\_$numerical$\_1\text{'},$ 'var'$))$

error$(\text{'}$The variable v$\_$numerical$\_1$ does not exist.$\text{'})$

end;

if $($~exist$(\text{'}$est$\_$error', 'var'$))$

error$(\text{'}$The variable est$\_$error does not exist.$\text{'})$

end;

if $($~exist$(\text{'}$h$\_$part$1\text{'},$ 'var'$))$

error$(\text{'}$The plot handle h$\_$part$1$ is missing. Please create it as instructed.$\text{'})$

end;

if $($~exist$(\text{'}$h$\_$part$2\text{'},$ 'var'$))$

error$(\text{'}$The plot handle h$\_$part$2$ is missing. Please create it as instructed.$\text{'})$

end;

if $($~exist$(\text{'}$h$\_$part$4\text{'},$ 'var'$))$

error$(\text{'}$The plot handle h$\_$part$4$ is missing. Please create it as instructed.$\text{'})$

end;

if $($~exist$(\text{'}$h$\_$part$6\text{'},$ 'var'$))$

error$(\text{'}$The plot handle h$\_$part$6$ is missing. Please create it as instructed.$\text{'})$

end;