function [ v_final ] = inelastic( m1, v1, m2, v2 )
%INELASTIC A function to calculate the final velocity of two
%objects that stick together after they collide.
%TUTORIAL PROGRAM#1 -- Created by R.Sonnenfeld, New Mexico Tech Physics
%Version 1.0  9/5/2005
%
%Inputs: 
%    m1, m2 are scalars which are mass of two objects in kg
%    v1, v2 are Matlab vectors (but not traditional physics vectors)
%    such that (v1(1)) is the magnitude of the velocity and
%              (v1(2)) is the angle the velocity makes with the x-axis
%    v2 applies to the second object.
%
%Outputs:
%   v_final is a two-component MATLAB vector such that
%       v_final(1) is the magnitude of the velocity and
%       v_final(2) is the angle the velocity makes with the x-axis
%
%Examples of Usage and results:
%>> inelastic(2,[1; 45],2,[1 ;45+180])
%ans =
%    0.0000
%  180.0000
%
%>> inelastic(2,[1; 45],2,[1 ;-45])
%v1_vec=
%    0.7071
%    0.7071
%v2_vec=
%    0.7071
%   -0.7071
%Momentum1=
%    1.4142
%    1.4142
%Momentum2=
%    1.4142
%   -1.4142
%v_final_vec =
%   0.7071
%         0
%ans =
%
%    0.7071
%         0
% Initialize
v_1mag=v1(1);  
v_1angle=v1(2);
v_2mag=v2(1);
v_2angle=v2(2);

%Convert angles to radians
v_1angle=v_1angle*pi/180;
v_2angle=v_2angle*pi/180;

%Calculate x,y components from magnitude and theta
v_1x=v_1mag*cos(v_1angle); %Calculate components
v_1y=v_1mag*sin(v_1angle);

v_2x=v_2mag*cos(v_2angle);  
v_2y=v_2mag*sin(v_2angle);

%Create Matlab vectors containing x and y components of velocity
v1_vec=[v_1x;v_1y];
v2_vec=[v_2x;v_2y];

disp('v1 in component form: v1_vec=');disp(v1_vec);
disp('v2 in component form: v2_vec=');disp(v2_vec);

%Calculate momentum vectors in x, y component form
p1_vec=m1*v1_vec;
p2_vec=m2*v2_vec;

disp('Momentum1 in component form: p1_vec=');disp(p1_vec);
disp('Momentum2  "  "      "  "  " p2_vec=');disp(p2_vec);

%Calculate total final momentum and velocity (in vector form)
ptot_vec=p1_vec+p2_vec;
v_final_vec=ptot_vec/(m1+m2)

%
%Convert final velocity from component form back to magnitude and angle
%form
v_final_mag=sqrt(v_final_vec'*v_final_vec);
v_final_angle=atan2(v_final_vec(2),v_final_vec(1));

%Convert final angle back to degrees
v_final_angle=180*v_final_angle/pi;

%Make a matlab vector out of the final magnitude and velocity
v_final=[v_final_mag;v_final_angle];