finding the distance between points

Hi! I'm studying for finals and I'm trying to rework a test problem. It's stumped me and I could use the help!

This is the problem:

Consider two airplanes that launch at the same moment and fly in the first quad of a 2-D space. Airplane A always travels at 800 km/h along a direction that makes a 20 degree angle with the x axis and originates at the coordinate origin. Airplane B always travels at 950 km/h in a direction that makes a 70 degree angle with the x axis and originates at 1000km in the x direction and 2000 km in the y direction. Make a function file that returns the distance between the two planes at a given time. Test your function at t=0,1, and 2 hrs.

I think I need to use either the norm function or the sqrt (x^2 + y^2) to find the distance but I'm kind of confused how to bring in the speed and what not into the equation. PLEASE HELP!

[Matt Kindig]

Write down (on paper) the equations for X and Y for each plane first. Hint:

X(t) = X0 + Vx*t  %x position at time t, velocity-x component

You should then be able to figure out how to calculate the distance from there. The sqrt(x^2+y^2) thing you had will help.

Answer 1

[Youssef Khmou]

hi,

the Dynamic 2D position is defined as :

X(t)=V*cos(theta)*t+X0 & Y(t)=V*sin(theta)*t+Y0 .

Try this version :

 theta_a=20*pi/180;
 theta_b=70*pi/180;
 Va=800; % Km/h
 Vb=950; % Km/h
 x0a=0;
 y0a=0;
 x0b=1000;
 y0b=2000;

 % Time simulation

 T=0:0.5:10; % 10 hours, we measure the distance every 30 minutes 
 % first airplane
 Xa=Va*cos(theta_a)*T+x0a;
 Ya=Va*sin(theta_a)*T+y0a;
 Xb=Vb*cos(theta_b)*T+x0b;
 Yb=Vb*sin(theta_b)*T+y0b;

 for t=1:length(T)

     D(t)=sqrt((Xa(t)-Xb(t)).^2+(Ya(t)-Yb(t)).^2);      
 end

 figure, plot(T,D), xlabel(' Time in Hours'), ylabel(' Distance /KM')
 title(' Distance between two airplanes a and b '), grid on

Try now to make it as function

[Youssef Khmou]

so the function take t as input

 Y=Yourfunction(t)

 %  Constantes 
 compute X(t) and Y(t)
 compute the distance D(X(t),Y(t))

......

Answer 2

[E]

Thank You! That made perfect sense. I knew it was a simple problem, I just couldn't remember how to solve it!