Projectile Motion with analytical and numerical analysis.
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Can someone help me fix the function? My last plot isn't plotting the curve.
%% HW3 Projectile Motion
clear; clc
%% Experimental
a=-9.8; %gravity
n=1; %interval
tt=10; %total time
T=0:n:tt; %time
% equation
x=T;
yy=a*(T); %F=m*a(t) neglecting mass
%% Analytic Analysis
% falling object without any drag coefficient and air density
%graph Velocity vs. Time
%% inputs
h=1; %step size
tl=0; %lower bound
th=10; %upper bound
vg=100; %initial velocity of golf ball (m/s)
%% establish domain
t=[tl:h:th]; %independent variable (time)
v= zeros(1,length(t)); %dependent variable (velocity)
%% initial condition
y(1)=vg;
%% constants
mg=1; %mass of golf ball
g=-9.8; %gravity
%% define function ODE
f=@(t,y) mg.*g; %Newton's Second Law equation is f=m.*a
%loop over N
for i=1:length(t)-1
% t(i+1)=t(i)+h; %Euler's Method
y(i+1)=y(i)+f(t(i),y(i)).*h;
end
%% Numerical Analysis
%consist of air density, cross sectional area, and Drag Coefficient of
%object
%% inputs
h=0.5; %step size
tl=0; %lower bound
th=10; %upper bound
vg=100; %initial velocity of golf ball (m/s)
%% establish domain
t=[tl:h:th]; %independent variable (time)
v= zeros(1,length(t)); %dependent variable (velocity)
%% initial condition
y(1)=vg;
%% constants
mg=2; %mass of golf ball
g=-9.8; %gravity
rho=1.225; %air density
Cg=0.47; %drag coefficient of a sphere
Ag=0.005; %cross-sectional area of golf ball
%% define function ODE
f=@(t,y) mg.*g; %Newton's Second Law equation is f=m.*a
%loop over N
for i=1:length(t)-1
% t(i+1)=t(i)+h; %Euler's Method
y(i+1)=y(i)+f(t(i),y(i)).*h;
end
fn=@(t,y) ((1/2.*mg).*(rho).*(Cg).*(Ag).*(vg.^2))+g;
for i=1:length(t)-1
yn(i+1)=y(i)+fn(t(i),y(i)).*h;
end
%% Plots
figure(1); clf(1)
plot(x,yy,'-.dr');
hold on
plot(t,y,'-o')
hold on
plot(t,yn,'--x')
title('Experimental and Analytic Analysis of a falling golf ball')
xlabel('Time (s)')
ylabel('Velocity (m/s)')
xlim([0 20])
ylim([0 25])

1 Comment
Image Analyst
on 15 Sep 2021
Edited: Image Analyst
on 15 Sep 2021
Need more detail. Exactly which variable (yy, y, or yn) is not plotting?
Why is the x axis x for one plot but t for the other two plots?
You don't need clf(1) right after you call figure(1) -- it's already clear/blank!
If you get rid of the calls to xlim and ylim, the plot looks like this:

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