module common

public :: initial,euler,print_table

integer, public, parameter :: double = 8
real (kind = double), public :: y,v,a,t,dt
real (kind = double), public, parameter :: g = 9.8

contains

subroutine initial()
   t = 0                ! initial time (sec)
   y = 10               ! initial height (m)
   v = 0                ! initial velocity
   a = -g
   print *, "time step dt ="
   read *, dt
end subroutine initial

subroutine euler()
   y = y + v*dt         ! use velocity at beginning of interval
   ! following included to remind us that acceleration is constant
   a = -g               ! y positive upward
   v = v + a*dt
   t = t + dt
end subroutine euler

subroutine print_table(nshow)
   integer, intent (in out) :: nshow
   if (t == 0) then
      print *, "number of time steps between output = "
      read *, nshow
      print "(t8,a,t24,a,t34,a,t48,a)", "time","y","velocity","accel"
      print *, ""
   end if
   print "(4f13.4)", t,y,v,a
end subroutine print_table

end module common

program free_fall            ! no air resistance
use common
   integer :: nshow,counter
   call initial()            ! initial conditions and parameters
   call print_table(nshow)   ! print initial conditions
   counter = 0
   iterate: do
      if (y <= 0) then
         exit iterate
      end if
      call euler()
      counter = counter + 1
      if (modulo(counter,nshow) == 0) then
         call print_table(nshow)
      end if
   end do iterate
   call print_table(nshow)   ! print values at surface
end program free_fall