# include <stdio.h>
# define g 9.8

main()
{
/*  
Step 1. Document and Declare Variables  
        
This program uses a discrete in time mathematical model defined by
Equations (3a,b) and (4a,b) of 
   http://www.krellinst.org/AiS/textbook/unit2/rock.html .

The input variables are:
     z0, the initial height of the rock
     v0, the initial velocity of the rock
     h, the time step 
     imax, the maximum number of time steps to calculate

The output variables are:
     ti, the time value at the i-th grid point
     zi, the rock height at ti
     vi, the rock velocity at ti

The auxiliary variables used are:
     vi_left, the velocity at time ti -.5*h
     vi_right, the velocity at time ti + .5*h
     i, a loop counter
*/

double vo,z0,h;
int imax;

double ti,vi,zi;

double vi_left,vi_right;
int i;

/*
Step 2. Initialize numerical solution at t = 0
*/
ti = 0;
printf("enter the rock's initial height in meters   ");
scanf("%lf",&zi);
printf("enter the rock's initial velocity in meters/second   ");
scanf("%lf",&vi);
printf("enter the the time step in seconds   ");
scanf("%lf",&h);
printf("enter the the maximum number of time steps to compute   ");
scanf("%d",&imax);

/*
Step 3. Calculate velocity at t = .5*h
*/
vi_left = vi -.5*g*h;

/*
Step 4. Begin time stepping
*/
for(i=0;i<=imax;i++)
  {

/*
Step 5. Advance solution one time step
*/
  ti = ti + h;
  zi = zi + vi_left*h;
  vi_right = vi_left - g*h;
  vi = .5*(vi_left + vi_right);
 
/*
Step 6. Output numerical solution
*/
  if(zi <= 0){
    printf("the rock is on the ground\n");
    break;
    }
    printf("%lf  %lf  %lf\n",ti,zi,vi);

/*
Step 7. Prepare for next time step
*/
  vi_left = vi_right;
  }

}