! Name: Nicholas Farkash
  ! Purpose: To write a program with an intrinsic function
  ! Date: September 13, 2021
  ! Due: September 17, 2021 at 6:00 PM

! Note: The two kinetic energies do not always agree. For smaller speeds,
! the reletavistic calculation returns a value of zero. This is because
! it calculates a small value divided by a large number, producing a very
! small number. This very small number is rounded off to zero, as Fortran
! cannot accurately store all of these numbers. This produces gamma equal
! to 1, which produces a KE of magnitude zero.

program HW_4
  implicit none

  real :: speed                         ! in m/s
  real :: mass                          ! in kg
  real, parameter :: C = 2.99792458e8   ! Speed of light in m/s

  real :: gamma               ! The Lorentz factor
  real :: gamma_root          ! The sqrt function of Lorentz factor
  real :: ke_nonrel           ! Non-relativistic Kinetic Energy
  real :: ke_rel              ! Relativistic Kinetic Energy
  
  write(*,*) "Enter a mass in kilograms."
  read(*,*) mass

  write(*,*) "Enter a speed in meters per second."
  read (*,*) speed

  gamma_root = sqrt(1 - ((speed**2)/(C**2))) !Broken up into two parts
  gamma = 1 / gamma_root                     !For easier calculations
  
  ke_rel = mass * C**2 * (gamma - 1)
  ke_nonrel = (mass * speed**2) / 2.0

  write(*,*) "The relativistic kinetic energy is",ke_rel,"joules."
  write(*,*) "The non-relativistic kinetic energy is",ke_nonrel,"joules."
  
  stop 0
end program HW_4