A code and plot a graph for a projectile motion of a ball

How do I write a code and plot a graph for a projectile motion of a ball thrown at 60 deg with a speed of 50 m/s using ode and runge kutta method.

Somebody please help

[KSSV]

Show us the code you have attempted.

[TANAMAY KOTHARI]

I dont know how to begin.

[TANAMAY KOTHARI]

i have the ode equations ready but dont know how to use them in matlab to plot the graph

[Scott MacKenzie]

Convert your ode equations to equations for the x and y position of the ball, then use plot(x,y).

[TANAMAY KOTHARI]

% x''=0, x(0)=0, x'(0)=Vx
% y''=-g, y'(0)=Vy, y(0)=0
clc
clear all
% constants
g=9.81; %gravity acc
v=50; % speed in m/s
angle= 60;%in deg
Vx=v*cosd(angle);
Vy=v*sind(angle);
h=0.1;
t(1)=0;
x(1)=0;
y(1)=0;

f=@(t,x,y) Vx*t;
g=@(t,x,y) Vy*t-0.5*g*t^2;

for i=1:100;
   l1=h*f(t,x);
   k1=h*g(t,y);
   l2=h*f(t+h/2,x+l1/2);
   k2=h*g(t+h/2,y+k1/2);
   l3=h*f(t+h/2,x+l2/2);
   k3=h*g(t+h/2,y+k2/2);
   l4=h*f(t+h,x+l3);
   k4=h*g(t+h,y+k3);
   x(i+1)=x(i)+(l1+2*l2+2*l3+l4)/6;
   y(i+1)=y(i)+(k1+2*k2+2*k3+k4)/6;
   t(i+1)=t(i)+h;
   fprintf('i=,t=,x=,y=\n',i,t,x,y)
plot(x,y)
end
   

This is the code I was able to come up, but the plot that appears comes blank.

[Scott MacKenzie]

You state that "the plot that appears comes blank". But, actually, there is no plot generated because the plot function never executes. You've got bugs in your code. Good luck.

BTW, you might want to have a look here -- a related question.

Answer 1

[James Tursa]

Your main problem is that you don't have enough state variables. You have these two equations:

x'' = 0

y'' = -g

That's two 2nd order equations, so you need to have 2 * 2 = 4 state variables. The state variables you need to integrate are x, y, Vx, Vy. But you only integrate two of these state variables, x and y. You have no code for integrating Vx and Vy. You need to add code for integrating Vx and Vy.

You also are using the solution of x and y integration as the derivative functions, which is incorrect. For a Runge-Kutta method, just use the derivatives. The code would be patterned after:

x' = Vx

y' = Vy

Vx' = x'' = 0

Vy' = y'' = -g

You also use g for both gravity and a function handle, so to avoid confusion you might want to change one of these.