MATLAB - Projectile motion by Euler's method

%Projectile motion
%By Mahesha MG
v0= input('Initial velocity(m/s): ');
a= input('Angle of projection(in degrees): ');
h= input('Time step (in seconds): ');

a=a*pi/180;
g=9.8;  %acceleration due to gravity in m/s^2
xmax=v0^2*sin(2*a)/g;
ymax=v0^2*sin(a)^2/(2*g);
td=2*v0*sin(a)/g;           %total time
x1=0;
y1=0;
figure('color','white');
for t=0:h:td+h
    x=v0*t*cos(a);          %analytic solution for x
    y=v0*t*sin(a)-g*t^2/2;  %analytic solution for y

    plot(x,y,'r*',x1,y1,'bo')
    hold all
    xlim([0 1.1*xmax]);
    ylim([0 1.1*ymax]);
    title('Projectile Motion By Mahesha MG');
    xlabel('Distance in meter');
    ylabel('Height in meter');
    getframe;
    x1=x1+h*v0*cos(a);      %Euler's method for x

    y1=y1+h*(v0*sin(a)-g*t);%Euler's method for y
end

Published with MATLAB® 7.13

SAMPLE OUTPUTS

Initial velocity(m/s): 10

Angle of projection(in degrees): 45
*** Analytic     ooo Numerical

(a) Time step (h) = 0.04s

(b) Time step (h) = 0.02s

(c) Time step (h) = 0.01s

(d) Time step (h) = 0.001s