Create an animation to show that the ship is safe.

An enemy submarine determined to sink your ship is sitting, torpedoes armed, exactly halfway between you and your home port. The submarine submerges to some fixed depth, and your ship now has no further information about its position. The enemy sub has to be directly underneath your ship to sink it — but the sub can track your moves with precision and respond efficiently. If your ship is fast enough, though, you will be able to set a wide course around the sub and reach port safely.

How much faster than the sub does your ship have to be to guarantee you can avoid the sub and get home?

I am trying to create ananimation for this . I am struggling. This is what I tried.

Couldyou please help me out.

theta = linspace(-pi,pi);
xc = cos(theta);
yc = -sin(theta);
plot(xc,yc);
axis equal
xt = [1 0.5 -1];
yt = [0 -0.4 0];
hold on
t = area(xt,yt); % initial flat triangle
hold off
for j = 1:length(theta)-10
    xt(2) = xc(j); % determine new vertex value
    yt(2) = yc(j);
    t.XData = xt; % update data properties
    t.YData = yt;
    drawnow limitrate % display updates
 

[Ntombikayise Bhengu]

https://fivethirtyeight.com/features/can-you-escape-the-enemy-submarines/ theanimationshould look like this one. I want to create itusing Matlab. The answer or the speed was found to be 2.33 times faster.

[mahesh kumar]

did u try fanimator??

[Ntombikayise Bhengu]

No I didnt let me google it

[mahesh kumar]

%%try this::

clc
clear 
close all
r=2.3326; %change ratio
theta=asin(1/r);
eps=0.0000001;
mtime=10/r;
syms x t

hold on
fanimator(@fplot,cos(x)*(t+eps),sin(x)*(t+eps),[-pi pi],'Color','red')
axis equal

fanimator(@fplot,(cos(theta)*r*x-10),sin(theta)*r*x,[0 t])  %%this optimisation equtation trickyy??
f = @(t) plot(cos(theta)*r*t-10,sin(theta)*r*t,'b*');
fanimator(f)

f = @(t) plot(10,0,'g*');
fanimator(f)

playAnimation
% vidObj = VideoWriter('urFile','MPEG-4');
% open(vidObj)
% writeAnimation(vidObj)
% close(vidObj)

[Ntombikayise Bhengu]

Thank you so much it is so helpful

[Ntombikayise Bhengu]

It works.

[mahesh kumar]

the ships path,a part is okay, other part may be a spiral,

[Ntombikayise Bhengu]

Do you have an idea of HowI can make it go around so that thestraigthline isnot just astraight line but also a curve and a straigth line?

[mahesh kumar]

i just think it backwards.. the ship and sub marine in an optimal condition,start at port, and the ship travels along the border of the submarines path.

So the spiral path can be traced as a point on the growing circle at 2.3326 times the velocity of submarine..

Am I correct??

[mahesh kumar]

clc 
clear
close all
syms x t
axis equal
hold on
fanimator( @(t) plot(t*(t-sin(t)), t*(1-cos(t)), 'ro'))
playAnimation  

adjust speed ; fom theta= pi/2; new path,

[Ntombikayise Bhengu]

Thank you so much. Yes this also helps a lot.

[mahesh kumar]

solve this problem