ME3255_HW3_roots.m

%ME3255 Homework 3
%Ryan Hyatt
%See README.m
%TODO - A better description.

clc
clearvars

vmag = 5; %input initial speed.
height = 1.27; %target height.
y0 = 1.72; %the initial height of the projectile.
a = -9.81; %downward acceleration due to gravity.
delta_x = 2.37; %horizontal displacement

es = 1e-5;%accuracy?
dx = 1e-6;
maxiter = 10000;

guess = 25; % value of initial guess, if the function requires one.

thetas = linspace(15,65);
heights = ones(1,length(thetas));
i = 0;

for i = 1:length(thetas)
    heights(i) = projectile(thetas(i), vmag)-height;
end

plot(thetas, heights)
    
%Newton's method.
[root(1),ea(1),iter(1)] = newtraph(@(theta) projectile(theta, vmag) - height,...
    @(theta) dprojectile_dtheta(theta, vmag),...
    guess, es, maxiter) % 1

%False Position Method
xl = 0;
xu = 30;

[root(2),fx,ea(2),iter(2)]=falsepos(@(theta) (projectile(theta, vmag) - height)...
    ,xl,xu,es,maxiter) %2

%Bisect Method
[root(3),fx,ea(3),iter(3)]=bisect(@(theta) (projectile(theta, vmag) - height)...
	,xl,xu,es,maxiter) %3

%Modified Secant
[root(4),ea(4),iter(4)]=mod_secant(@(theta) (projectile(theta, vmag) - height),...
    dx,guess,es,maxiter) %4

table = [root',ea',iter']