# finding intercept point in the plot

6 views (last 30 days)
FRANCISCO CORTEZ on 8 Apr 2021
Answered: Image Analyst on 22 May 2022
close all
theta = 50;
v0=200;
slope= 0.1;
vx=v0*cosd(theta); %horizontal component of velocity vector
vy=v0*sind(theta); %vertical component of velocity vector
g=9.807;
tf=2*vy/g; %total flight time
t=linspace(0,tf,150);
for r=1:length(t)
x(r)=vx*t(r); %horizontal postion
A(r)=vy*t(r)-0.5*g*t(r)^2; %vertical postion of particle
R(r)=x(r)*slope; %vertical postion of terrain
end
figure(1)
plot(x,A,'b')
hold on
plot(x,R,'m')
title('Altitude VS Range')
xlabel('Range')
ylabel('Altitude')
legend({'Range','Line of Terrain'},'Location','southwest')
grid on
hold on

Star Strider on 8 Apr 2021
Try this:
theta = 50;
v0=200;
slope= 0.1;
vx=v0*cosd(theta); %horizontal component of velocity vector
vy=v0*sind(theta); %vertical component of velocity vector
g=9.807;
tf=2*vy/g; %total flight time
t=linspace(0,tf,150);
for r=1:length(t)
x(r)=vx*t(r); %horizontal postion
A(r)=vy*t(r)-0.5*g*t(r)^2; %vertical postion of particle
R(r)=x(r)*slope; %vertical postion of terrain
end
[Amax,idx] = max(A);
x_int = interp1(A(idx:end)-R(idx:end), x(idx:end), 0);
y_int = interp1(x, R, x_int);
figure(1)
plot(x,A,'b')
hold on
plot(x,R,'m')
plot(x_int, y_int, 'rs')
title('Altitude VS Range')
xlabel('Range')
ylabel('Altitude')
legend({'Range','Line of Terrain','Intercept'},'Location','southwest')
grid on
hold off
.
Star Strider on 13 Apr 2021
s always, my pleasure!

FRANCISCO CORTEZ on 12 Apr 2021
How can i determine the initial angle of the projectile with respect to the horizontal in order to achieve maximum range

Image Analyst on 22 May 2022
See attached demo that computes just about everything you could ever want to know about a projectile.