Question

Using MATLAB to plot the trajectory of a projectile:

Consider a cannon launching a cannonball at initial velocity, v, towards a wall. With an elevation of launch angle, θ, distance to wall, D, and wall height, h.

Write a MATLAB function to plot the trajectory of the cannonball and return information in the following form:
>> [outcome, impact] = Q3 STNO(v,theta,D,h)

where v, theta, D and h are the launch velocity (m/s), launch angle (radians), distance to wall (m) and height of wall (m) as stated above. For the case where the ball lands before reaching the wall, outcome should be set to 0 (zero) and impact to NaN. If the ball strikes the wall, then outcome should be 1 (one) and impact should be the height above the ground where the ball hits the wall. Finally, for the case where the ball overshoots the wall, outcome should be set to 2 and impact to NaN.  Keep all inputs positive and θ < π/2.

Answer 1

MATLAB function

function [outcome, impact] = Q3STNO(v,theta,D,h)
g=9.81;
D=linspace(0,D,100);
vertical_distance=tand(theta)*D-(g*D.^2/(2*v^2*cosd(theta)^2));
if vertical_distance(end)<=0
outcome=0;
impact=NaN;
disp('No impact')
elseif vertical_distance(end)>0 && vertical_distance(end)<=h
outcome=1;
impact=vertical_distance(end);
disp('Impact happened')
else
outcome=2;
impact=NaN;
disp('Overshoot')
end
plot(D,vertical_distance)

Script to call function (Result shown for all three cases by varying angle of throw)

clc
clear
close
v=10; %initial velocity
theta=60; %Angle of throw
D=4; % Distance of wall
h=3; % height of wall
[outcome, impact] = Q3STNO(v,theta,D,h)