Question

If a cannonball is shot at A and needs to land at B. What should be the inclination angle α for the firing? Use MATLAB to plot the x‐y positions of the cannonball from the origin at A till it lands at B for both cases. Please help with the MATLAB part only.

Answer 1

%Please change value of landing coordinate X &Y and

%initial velocity v0 in program as per your requirement

clc
clear all

%% Below put X and Y coordinate of langing point
% assuming firing point as origin
%calculation of angle alpha
X=40.2; % in meter
Y=0; % in meter

v0=20; % m/s

%calculation starts here
g=9.81;
K= g/(2*v0^2);
syms theta_r
theta_r=solve(X*tan(theta_r)==Y + K*(X/cos(theta_r))^2,theta_r);
theta_d=radtodeg(theta_r);
alpha_degree=double(theta_d);
alpha_degree=real(alpha_degree);
alpha_degree=alpha_degree(alpha_degree>0)
%% plot of trajectory path
alpha_degree = transpose(alpha_degree);
num_of_roots=size(alpha_degree, 2);
x=0:X/200:X;
for i=1:num_of_roots
y = x*tand(alpha_degree(i))-K*(x/cosd(alpha_degree(i))).^2;
plot(x,y);
hold on
end
xlabel('x ( m)');
ylabel('y ( m)');
grid on
title('Trajectory of cannonball');