Using Euler's Method for projectile motion

Problem statement: Write a program that employs the Euler method to compute the solution to the freely falling object. That is, calculate 𝑣 as a function of time. Consider different starting velocities over a time range from 𝑡 = 0 to 𝑡 = 10 s.

I'm not sure how to set up my time interval from 0-10 sec. I'm guessing "for j = t(1):dt:tf ". But not fully sure how to proceed. Any help would be appreciated. Thnak you.

What I have so far:

clear;

N = 100; % points to be taken

g = 9.8; % acceleration due to gravity (m/s^2)

dt = 0.01; % time step for time range of 1-10 sec.

theta = input('Angle of projection(in degrees): '); % Allows user to input

h = input('Initial height (in meters): ');

v_0 = input('Initial velocity (in m/s): ');

% Initial conditions below

x(1) = 0; % intial x position (m)

y(1) = h; % intial y position (m)

t(1) = 0; % inital time (s)

tf = 10; % final time (s)

v(1) = v_0; % initial velocity (m/s)

v_x = v_0*cos(theta); % "x" component of the velocity

v_y = v_0*sin(theta); % "y" component of the velocity

v_x(1) = v_x;

v_y(1) = v_y;

n = 1;

while n < N

% for statement here?

v(n+1)=sqrt((v_x(n)^2)+(v_y(n)^2));

v_x(n+1) = v_x(n);

v_y(n+1) = v_y(n) - g*dt;

x(n+1) = x(n) + v_x(n)*dt;

y(n+1) = y(n) + v_y(n)*dt;

if y(n+1)<0

n = N;

else

n = n+1;

end

end

Answer 1

[Alan Stevens]

A little more like this? (I've used arbitrary values for initial conditions etc.)

N = 200; % points to be taken
g = 9.8; % acceleration due to gravity (m/s^2)
dt = 0.01; % time step for time range of 1-10 sec.
theta = 45; %input('Angle of projection(in degrees): '); % Allows user to input
h = 1;  %input('Initial height (in meters): '); 
v_0 = 5; %input('Initial velocity (in m/s): ');
% Initial conditions below 
x(1) = 0; % intial x position (m)
y(1) = h; % intial y position (m)
t(1) = 0; % inital time (s)
tf = N*dt; % final time (s)
v(1) = v_0; % initial velocity (m/s)
v_x = v_0*cos(theta); % "x" component of the velocity
v_y = v_0*sin(theta); % "y" component of the velocity 
v_x(1) = v_x;
v_y(1) = v_y;
n = 1;

for n = 1:N
    v(n+1)=sqrt((v_x(n)^2)+(v_y(n)^2));
    v_x(n+1) = v_x(n);
    v_y(n+1) = v_y(n) - g*dt;
    x(n+1) = x(n) + v_x(n)*dt;
    y(n+1) = y(n) + v_y(n)*dt;
    t(n+1) = t(n) + dt;
    if y(n+1)<0
       break 
    end
end
   
plot(x,y),grid
xlabel('x'),ylabel('y')

[jcc]

ah, but I'm still not sure how to incorporate the time scale from 0-10 sec. Because n = 1:N would be 1-200 right?

[Alan Stevens]

Set N = 10/dt

[jcc]

ok, thank you for your help!