% Solve the ``softball'' problem using a shooting method combined with 
% the secant algorithm. To find: the ball's launch velocity given a 
% maximum elevation of ypeak.

close all
clear all
clc

global Cd Uwind g ypeak

% Variable input (mks units where appropriate).
Uwind = 13.0/3.6;
g = 9.8;
Cd = 0.037;
theta0 = 24.7*pi/180.0;
ypeak = 5.2;
% End of variable input.

% Specify initial guesses for launch speed.
U1 = 10.0;
U2 = 40.0;

% Use secant-type algorithm to find the launch velocity that gives a
% maximum elevation of ypeak.
f1 = softball_function(U1,theta0);
f2 = softball_function(U2,theta0);
delta = U2-U1;
count = 1;    % Initialize counter.
while ( (abs(delta)>1e-6) && (count<1001) )
 U3 = U1-f1*(U2-U1)/(f2-f1);
 fprintf('Iteration=%2.0f\t, Current root estimate=%12.8f\n',count,U3);
 delta = U3-U2;
 U1 = U2; f1 = softball_function(U1,theta0);
 U2 = U3; f2 = softball_function(U2,theta0);
 count = count+1;
end

if count==1000
 fprint('Maximum number of iterations reached.');
else
 fprintf('Release velocity (m/s) =%12.8f\n',U3); 
end