clc$\%$clears console

clear all$\%$clears the history

v$=200$;$\%$initialize velocity as $0$

theta$\_1=50$;$\%$initialize theta$1$ as $50$

g$=9\mathrm{.}81$;$\%$initialize gravity as $9\mathrm{.}81$

k$=(2*$v$*$sind$($theta$\_1))/$g;$\%$time to get back on earth if there was no slope

for i$=0$:$0\mathrm{.}01$:k$\%$calculate x and h in $0\mathrm{.}01$ tep

if$((($v$*$sind$($theta$\_1)*$i$)-(0\mathrm{.}5*$g$*$i$.*$i$)-0\mathrm{.}1*$

$($vcosd$($theta$\_1)*$i$))<0)$

def$=$i;$\%$if it touchees or goes after the line

then break

break;

end

end

z$1=($v$*$cosd$($theta$\_1)*$def$)$;

z$2=($v$*$sind$($theta$\_1)*$def$-(0\mathrm{.}5*$g$*$def$.*$def$)$;

plot$(($v$*$cosd$($theta$\_1)*$def$),$

$($v$*$sind$($theta$\_1)*$def$)-$

$(0\mathrm{.}5*$g$*$def$.*$def$),\text{'}$or$\text{'})$;$\%$plot that point

text$($z$1,$z$2[(\text{'}$ num$2$str$($z$1)$;; num$2$str$($z$2)\text{'})\text{'}])$;

hold on

T$=0$:$0\mathrm{.}1$:def;

X$1=($v$*$cosd$($theta$\_1)*$T$)$;

H$1=($v$*$sind$($theta$\_1)*$T$-(0\mathrm{.}5*$g$*$T$.*$T$)$;

plot$($X$1,$H$1,\text{'}$c$\text{'})$;$\%$plot the slope

hold on

xlabel$(\text{'}$range $($meters$)\text{'})$;

ylabel$(\text{'}$distance $($meters$)\text{'})$;

legend$([\text{'}($X$=\text{'}$ num$2$str$($z$1)$;$,$ Y$=\text{'}$

num$2$str$($z$2)$;$)\text{'}])$;

A$=0$:$0\mathrm{.}01$:$4000$;

B$=(1/10)*$A;

plot$($A$,$B$)$;

hold off;

disp$(\text{'}$Theta for max range is: $\text{'})$;

alpha$=$atand$(0\mathrm{.}1)/2$;

theta$=45+$alpha

disp$(\text{'}$Maximum range is: $\text{'})$;

R$=(($v$*$v$)/($g$*$cosd$($alpha$)*$cosd$($alpha$)))*(1-$

sind$($alpha$))$

$\%$At theta$=47\mathrm{.}8553\backslash$deg $,$ there would be maximum range.