Dynamics Problem using two moving object

2017 10 27
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更新时间：2017 10 30
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I've been having problems solving this equation in MATLAB. Solving on paper is more intuitive to me and I'm struggling in making the language jump. So far, here is my code:
pA = [0 14]; %position of ship A at start
pB = [-25 0]; %position of ship B at start
vA = [0 -7]; %velocity of ship A at start
vB = [16 0]; %velocity of ship B at start
for t=1:4;
dA=(pA+vA*t) %position of A based on time
dB=(pB+vB*t) %position of B based on time
end
I can't seems to figure out how to get the positions of each of the ships in relation to each other. Once I do that, I was attempting to use the zeros function to solve for the 8 mile visibility. couldn't get it to work. Thanks for your help!

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Birdman
Birdman 2017-10-27
编辑：Birdman 2017-10-27

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You can find position of A with repsect to B by the following:
pAwrtB=dA-dB;%position of A with repsect to B
vice versa:
pBwrtA=dB-dA;%position of B with repsect to A
Because imagine every time we spot our position on the x-y coordinate axis, we actually reference to the origin and to this
dOurPosition - [0 0]
But in this situation, relative positions are found just as above. Change the for loop like this:
for t=1:4
dA=pA+vA*t;
dB=pB+vB*t;
pBwrtA=dB-dA;%position of B with repsect to A
pAwrtB=dA-dB;%position of A with repsect to B
end

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BlkHoleSun
BlkHoleSun 2017-10-27
Thank you for the help. I've taken what you've taught me and continued to plug away at it. I have one remaining question. I can't figure out how to make my y-axis span the time from 07:00 to 11:00 in one hour increments. Below is my code and you'll see that I'm very close to figuring it out. I believe the problem is in the way I've defined 't'.
%Defining the variables
pA = [0 14]; pB = [-25 0];
vA = [0 -7]; vB = [16 0];
t=linspace(0,4,100);
dT=zeros(size(t));
%compute a loop for the distance
for i=1:length(t)
dA=pA+vA*t(i);
dB=pB+vB*t(i);
dT(i)=sqrt(dA(2).^2+dB(1).^2);
end
%Identify the row and column for when the distance is less than 8
[r, c]=find(dT<=8);
x1=t(min(c)); x2=t(max(c));
%plot distance curve and visibility line
hold on
plot(t, dT)
plot(t,8*ones(size(t)))
%label graph and add text string
xlabel('\bf\itTime, hours+7am \rm');
ylabel('\bf\itDistance, miles\rm');
z=text(.1,40,['The ships will see each other between the times of ' num2str(x1), 'and ', num2str(x2)'.']);
datetick('x', 'HH:MM');
BlkHoleSun
BlkHoleSun 2017-10-27
Correction: I can't figure out how to make my x-axis span the time from 07:00 to 11:00 in one hour increments.
Birdman
Birdman 2017-10-30
Use the m file. I used xticklabels to do it.
BlkHoleSun
BlkHoleSun 2017-10-30
Thanks for the help. I've learned a lot about graphing this problem!

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