; Combine the equations for conservation of momentum and kinetic energy
; to solve for the resulting velocity of two objects colliding head on.
clear all
; equations for energy:
e1=1/2*mass1*velocity1_old^2
e2=1/2*mass2*velocity2_old^2
e3=1/2*mass1*velocity1_new^2
e4=1/2*mass2*velocity2_new^2
e1+e2=e3+e4
eliminate all
; equations for momentum:
#1: u1=mass1*velocity1_old
#2: u2=mass2*velocity2_old
#3: u3=mass1*velocity1_new
#4: u4=mass2*velocity2_new
u1+u2=u3+u4
eliminate all
clear 1-4
eliminate velocity1_new
velocity2_new
simplify
velocity2_new = ((sign*((mass1*(velocity1_old-velocity2_old))^2)^.5)+(mass1*velocity1_old)+(mass2*velocity2_old))/(mass1+mass2)
compare 6