%Written by: Taylor Poon, ID: 30750539
%Created: 18/09/19
%ball trajectory using secant method
clear all; close all; clc;

%variables
% v0 = initial velocity
% y0 = thrower's elevation
% x = distance from the thrower to the catcher
% y = catcher's elevation
% tangle = throwing angle
% ptangle = angle previous to throwing angle
% g = gravitational acceleration
% precision = precision used to decide if value is close enough to the root
v0 = 20;
y0 = 2;
x = 35;
y = 1;
g = 9.81;


%trajectory of a thrown ball anonymous function
theta = linspace(0,60);
f = @ (theta) tand(theta).*x - g ./ (2*v0^2.*cosd(theta).^2) * x^2 + y0 - y;

%call secant function
xi = 15;
xi_1 = 60;
precision = 1e-4;

[root, iter] = secant(f,xi,xi_1, precision);

plot(theta, f(theta));
title('angle of thrown ball trajectory');
xlabel('theta (degrees)');
ylabel('thrown ball trajectory equation');
hold on
plot(root,f(root), 'kd');
fprintf('The initial throwing angle required is %2.f degrees and the number of iterations taken is %2.f.', root, iter);

%plot root-finding equation
% df = @ (theta) tand(theta) - g ./ (v0^2 .* cosd(theta).^2) * x;
% [root_min, iter_min] = secant(df, xi, xi_1, precision);
% hold on
% root_min %check this, maybe equation is wrong?
% plot(root_min,f(root_min), 'bd');