How do I get a plot of a parabola graph from the mathematical model(trajectory of a particle) given?
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Hi.
I am having a bit of a problem getting the graph of this mathematical model. The graph that I am supposed to get is a parabola showing the trajectory of a particle with drag.(I do get a parabola for the trajectory of the particle without drag.) Instead I keep getting half of a parabola.
I have tried changing the parameters but I still can't seem to get the parabola. The v(velocity),theta(launch angle),r(radius of particle) and x0(initial position) can be changed below.
I would really like some help here.
The equation of the trajectory of the particle with drag is:
x(t) = v_∞ t + m/k (v_0 – v_∞ )(1 - e ^(-kt/m)) + x_0.
The codes for the model that I have written is:
clc; close all; clear all;
% Flight trajectory computation
% Initial values
g = 9.81; % gravity, m/s^2
v = 40; % launch velocity, m/s
theta = 55 * pi/180; % launch angle, radians
m = 5.5*10^-7;
u = 1.78*10^-5;
r = 0.001;
k = 6*pi*u*r;
vinf = m*g/k;
x0 = 20;
% Compute and display results
disp('time of flight (s):') % label for time of flight
tg = 2 * v * sin(theta)/g % time to return to ground, s
disp('distance traveled (ft):') % label for distance
xg = v * cos(theta) * tg % distance traveled
% Compute and plot flight trajectory
t = linspace(0,tg,5000);
x = v * cos(theta) * t;
%y = v * sin(theta) * t - g/2 * t.^2; %trajectory of a particle without drag
y = vinf * sin(theta) * t - m/k * (v * sin(theta) - vinf* sin(theta) * (g/2 * t^2))*(1 - exp(-(k*t)/m)) + x0; %trajectory of a particle with drag
plot(x,y) , axis equal, axis([ 0 300 0 100 ])
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