How to find if a projectile intersects a point in a line?

This is my uni assignment. I have to make an angry birds like game. I have created most of it but im kind of stuck at how to tell if ive "hit the target". We were given a matrix equation type thing of how to work out if lines intersect but im not sure how to use that with my projectile?

Also is there a way to have a margin of error, like thats close enough.

I have points of intersection of the ground and the target set to xi, yi. for the margin of error can you do something like yt1 == yi +- 5?

Thanks for the help. I've included my full code below.

clc; clear all; close all;

x1 = 0;
y1 = 50;
x2 = 1000;
y2 = 50;
x3 = 725;
y3 = 49;
x4 = 725;
y4 = 51;

MatrixA = [x1 x2 x3; y1 y2 y3; 1 1 1];
MatrixB = [x1 x2 x4; y1 y2 y4; 1 1 1];
MatrixC = [x1 x3 x4; y1 y3 y4; 1 1 1];
MatrixD = [x2 x3 x4; y2 y3 y4; 1 1 1];

if det(MatrixA)*det(MatrixB) < 0 && det(MatrixC)*det(MatrixD) < 0
xi = ((x4-x3)*(x2*y1-x1*y2)+(x2-x1)*(x3*y4-x4*y3))/((x2-x1)*(y4-y3)-(x4-x3)*(y2-y1));
yi = ((y4-y3)*(x2*y1-x1*y2)+(y2-y1)*(x3*y4-x4*y3))/((x2-x1)*(y4-y3)-(x4-x3)*(y2-y1));
intersection = [xi yi];
%fprintf('Co-ordinates of intersection = (%0.2f %0.2f)\n', xi, yi)
else
    disp('False')
end

plot(xi,yi, '-p', 'MarkerSize', 20,...
    'MarkerEdgeColor', 'blue',...
    'MarkerFaceColor', 'red');
xlim([0,1000]);
ylim([0,500]);

hold on

ground_length = x1:x2;
ground = 0*ground_length + 50;
plot(ground, '-');


prompt1 = 'What is the firing angle? '; %asking for user to input the angle to fire at
theta1 = input(prompt1); 
prompt2 = 'What is the firing speed in m/s? '; %asking for the user to input the speed of the projectile
v01 = input(prompt2);

x0 = 0; %starting point on x axis
y0 = 50; %starting point on y axis
g = 9.81; %gravity. used positive as it gives wonky time numbers if using negative

tup1 = (v01*sind(theta1))/g; %working out the time to max height where vertical velocity = 0
maxheight1 = (v01^2*(sind(theta1)^2))/(2*g) + y0; %working out max height to work out time to hit ground, added y0 as that is the starting height
tdown1 = sqrt(2*maxheight1/g); %time to hit the ground from max height
tmax1 = tup1 + tdown1; %total flight time
t1 = 1:tmax1;

vx1= v01*cosd(theta1); %velocity in x diretion
vy1 = v01*sind(theta1); %velocity in y direction

xt1 = x0 + vx1*t1; %points in time of the projectile
yt1 = y0 + vy1*t1-0.5*g*t1.^2; %points in time of the projectile

plot(xt1,yt1)
title('Level 1 Angry Space Catapult')

Answer 1

[darova]

if min(D) < tolerance, disp("the target is destroyed"), end

[Andrew Mackintosh]

can you explain that at all so i can follow it?

also when i see my graphs for the projectile they are never joined at either end like yours. they always start and end in a floaty space. any idea why is that?

[darova]

Check distance between every point of your trajectory (xt1; yt1) and target (xi; yi)

I entered: 45 degrees, 80 m/s

[Andrew Mackintosh]

i dont fully understand the code.

dont you have to define min(D)?

tolerance, does that have a value? or do i need to put in a value for that?

[darova]

I mean your margin +-5 for example

D = sqrt( (xt1-xi).^2 + (yt1-yi).^2 );
margin = 5;
if min(D) < margin, disp("the target is destroyed"), end