/* program free_fall  C++ version */
#include <stdio.h>
#include <iostream.h>
#include <iomanip.h>
/* need iostream.h and iomanip.h for stream output using cin and cout */

void initial(double &y,double &v,double &a,double &g,double &t,
             double &dt);
void Euler(double &y,double &v,double &a,double g,double &t,
           double dt);
void print_table(double y,double v,double a,double t,int &nshow);

main()
/* no air resistance */
 {
     double y,v,a,g,t,dt;
     int counter,nshow;
/*   initial conditions and parameters */
     initial(y,v,a,g,t,dt);
/*   print initial conditions */
     print_table(y,v,a,t,nshow);
     counter = 0; 
     while (y >= 0)
        {
          Euler(y,v,a,g,t,dt);
          counter = counter + 1;
          if (counter % nshow == 0)
           print_table(y,v,a,t,nshow);
        }
       print_table(y,v,a,t,nshow);   // print values at surface
  } 

void initial(double &y,double &v,double &a,double &g,double &t,
             double &dt)
  {
      t = 0;       // initial time (sec)
      y = 10;      // initial height (m)
      v = 0;       // initial velocity
      g = 9.8;     // (magnitude) of accel due to gravity
      a = -g;
      cout << "time step dt = ";
      cin >> dt;   // read in value for dt
  }

void Euler(double &y,double &v,double &a,double g,double &t,double dt)
  {
/*     use velocity at beginning of interval */ 
       y = y + v*dt;
       a = -g;     // y positive upward          
       v = v + a*dt;
       t = t + dt;
   }

void print_table(double y,double v,double a,double t,int &nshow)
   {
    if (t == 0) 
      {
       cout << "number of time steps between output = "; 
       cin >> nshow; 
       cout << "\n  time (s) y (m)  velocity (m/s)   accel (m/s^2) "
            << "\n\n";
      }
      /* setw(n) allows n spaces for a number
         setprecision(m) provides m decimal places  */
       cout << setw(10) << setprecision(3) << t;
       cout << setw(10) << setprecision(3) << y;
       cout << setw(10) << setprecision(3) << v;
       cout << setw(12) << setprecision(3) << a << "\n";
    }