function archery$\_$game$()$

$\%$ Constants

g $=9\mathrm{.}81$; $\%$ acceleration due to gravity $($m$/$s$^2)$

$\%$ Set up figure

fig $=$ figure$(\text{'}$Position$\text{'},[200,200,800,600])$;

$\%$ Initialize archer position

archer$\_$x $=0$;

archer$\_$y $=1$; $\%$ Updated archer starting position

$\%$ Create sliders for angle and power

angle$\_$slider $=$ uicontrol$(\text{'}$Style$\text{'},$ 'slider', 'Min', $0,$ 'Max', $90,$ 'Value', $45,...$

'Position', $[100,50,300,20],$ 'Callback', @update$\_$plot$)$;

power$\_$slider $=$ uicontrol$(\text{'}$Style$\text{'},$ 'slider', 'Min', $1,$ 'Max', $20,$ 'Value', $10,...$

'Position', $[100,20,300,20],$ 'Callback', @update$\_$plot$)$;

$\%$ Create fire button

fire$\_$button $=$ uicontrol$(\text{'}$Style$\text{'},$ 'pushbutton', 'String', 'Fire', $...$

'Position', $[450,20,100,50],$ 'Callback', @fire$\_$arrow$)$;

$\%$ Set up axes

ax $=$ axes$(\text{'}$Parent$\text{'},$ fig, 'Position', $[0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}8,0\mathrm{.}7])$;

axis$($ax$,[050020])$; $\%$ Adjusted y$-$axis to accommodate the archer and target

xlabel$($ax$,$ 'Distance $($m$)\text{'})$;

ylabel$($ax$,$ 'Height $($m$)\text{'})$;

hold$($ax$,\text{'}$on$\text{'})$;

$\%$ Plot archer

archer$\_$plot $=$ plot$($ax$,$ archer$\_$x$,$ archer$\_$y$,\text{'}$b$.\text{'},$ 'MarkerSize', $20)$;

$\%$ Initialize arrow trajectory

arrow$\_$plot $=$ plot$($ax$,$ NaN, NaN, $\text{'}$r$-\text{'},$ 'LineWidth', $2)$;

$\%$ Play three rounds

for round $=1$:$3$

$\%$ Generate random target position

target$\_$x $=$ randi$([10,40])$;

target$\_$y $=1$; $\%$ Place target on ground level

target$\_$radius $=0\mathrm{.}5$;

$\%$ Plot target

target$\_$plot $=$ viscircles$($ax$,[$target$\_$x$,$ target$\_$y$],$ target$\_$radius, 'EdgeColor', $\text{'}$r$\text{'})$;

$\%$ Update plot based on slider values

update$\_$plot$()$;

$\%$ Wait for user input

uiwait$($fig$)$;

$\%$ Check if the archer hits the target

if check$\_$hit$($archer$\_$x$,$ archer$\_$y$,$ target$\_$x$,$ target$\_$y$,$ target$\_$radius$)$

disp$(\text{'}$You hit the target!$\text{'})$;

else

disp$(\text{'}$You missed the target.$\text{'})$;

end

$\%$ Remove target plot

delete$($target$\_$plot$)$;

end

$\%$ Close figure

close$($fig$)$;

$\%$ Update plot based on slider values

function update$\_$plot$($~$,$ ~$)$

$\%$ Get angle and power from sliders

angle $=$ get$($angle$\_$slider, 'Value'$)$;

power $=$ get$($power$\_$slider, 'Value'$)$;

$\%$ Calculate trajectory

time $=$ linspace$(0,2*$power$*$sind$($angle$)/$g$,100)$; $\%$ Assuming g $=9\mathrm{.}81$ m$/$s$^2$

xTrajectory $=$ archer$\_$x $+$ power $*$ cosd$($angle$)*$ time;

yTrajectory $=$ archer$\_$y $+$ power $*$ sind$($angle$)*$ time $-0\mathrm{.}5*$ g $*$ time.$^2$;

$\%$ Update arrow trajectory

set$($arrow$\_$plot, 'XData', xTrajectory, 'YData', yTrajectory$)$;

end

$\%$ Fire the arrow

function fire$\_$arrow$($~$,$ ~$)$

$\%$ Get angle and power from sliders

angle $=$ get$($angle$\_$slider, 'Value'$)$;

power $=$ get$($power$\_$slider, 'Value'$)$;

$\%$ Calculate trajectory

time $=$ linspace$(0,2*$power$*$sind$($angle$)/$g$,100)$; $\%$ Assuming g $=9\mathrm{.}81$ m$/$s$^2$

xTrajectory $=$ archer$\_$x $+$ power $*$ cosd$($angle$)*$ time;

yTrajectory $=$ archer$\_$y $+$ power $*$ sind$($angle$)*$ time $-0\mathrm{.}5*$ g $*$ time.$^2$;

$\%$ Update arrow trajectory

set$($arrow$\_$plot, 'XData', xTrajectory, 'YData', yTrajectory$)$;

$\%$ Enable next round

uiresume$($fig$)$;

end

$\%$ Check if the archer hits the target

function hit $=$ check$\_$hit$($archer$\_$x$,$ archer$\_$y$,$ target$\_$x$,$ target$\_$y$,$ target$\_$radius$)$

$\%$ Calculate distance between archer and target

distance $=$ sqrt$(($archer$\_$x $-$ target$\_$x$)^2+($archer$\_$y $-$ target$\_$y$)^2)$;

$\%$ Check if the distance is less than or equal to the target radius

hit $=$ distance $<=$ target$\_$radius;

end

end

$($Above is a code for an archery game. The problem is when I shoot the arrow at the target with the trajectory lined up$,$ it doesnt count as a hit. No matter how close or even on the target the arrow trajectory is$,$ it misses and I need it to properly tell the difference between a hit and a miss.$)$