%calculate the square of distance between A and (0, 0), and between B and
%(0, 0). Actually, we only care about the coefficients
A = [320^2, -2*320*800, 800^2]; % Location_A = 800 - 320*t
B = [160^2, -2*160*410, 410^2]; % Location_B = 410 - 160*t

%the square of distance between them
D = A + B;
x= [0: 0.1: 5];
f = polyval(D, x);

%determine when we get the min distance, with precision of 0.1
[a, i] = min(f);
%the index is i-1 because we start from time 0
time_to_reach_min_distance = (i-1)*0.1

%sqrt(f) is the real distance
%here, we got the bound from time_to_reach_min_distance
y = [0: 0.1: time_to_reach_min_distance];
g = polyval(D, y);
plot(y, sqrt(g))

E = D - [0, 0, 30^2];

%calculate the roots. While we have two root, we only keep the first one as
%stated in the problem
roots(E)