Caida libre, solucion exacta (creando archivos de datos en el codigo)

Consideremos el programa en c++

// caida_00.cpp
#include <iostream>
#include <complex>
#include <fstream> 
#include <sstream>
using namespace std;
double g   = 9.8;
int main()
{
 float y0,v0,y;
 float t,ti,tf,dt;int it,Nt=9; 
 y0	=	100.0;
 v0	=	0.0;
 
 ti	=	0.0;
 tf	=	5.0;
 dt	=	(tf-ti)/float(Nt);
 
 ofstream myfile00;myfile00.open ("cpp.dat");
 for(it=0;it<Nt;it++)
 {
  t	=	ti+dt*float(it);
  y	=	y0+v0*t-0.5*g*t*t;
  myfile00<<it<<" "<<t<<" "<<y<<"\n";
 }
 myfile00.close();

program newton_10
implicit none

real    :: y0,v0,y,g=9.8
real    :: t,ti,tf,dt
integer :: it,Nt=9

y0	=	100.0;
v0	=	0.0;
 
ti	=	0.0;
tf	=	5.0;
dt	=	(tf-ti)/real(Nt);

open(unit=10, file="fortran.dat")
do it   = 0,Nt
t	=	ti+dt*float(it)
y	=	y0+v0*t-0.5*g*t*t
write(10,*)it,t,y
enddo

end program

g	=	9.8
y0	=	100
v0	=	0

ti	=	0
tf	=	5
Nt	=	9
dt	=	(tf-ti)/Nt

f= open("python.dat","w")
for it in range(9):
  t	=	ti+it*dt
  y     =       y0+v0*t-0.5*g*t*t
  f.write(str(it)+" "+str(t)+" "+str(y) + "\n")
f.close()