#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double g = 9.81;
float y, to, E;

// First function ---------------

float f(float t)
{
return 	y - (g/2)*t*t;
}

float f_derivative(float t)
{
return  - g*t;
}

typedef float (*PFUN) (float);

float newton (PFUN f, float to, float E){
float ss = 0;
float c[41];
c[0] = to ;

int i,n = 40;
printf("\nThe T values: \n");

for(i=1;i<=n;i++)
{
c[i] = c[i-1] - f(c[i-1])/f_derivative(c[i-1]);
printf("%f \n", c[i]);
if (abs((c[i] - c[i-1])/c[i-1]) <= E/100.0 )
{
printf("\nThe solution is t =  %f degrees.\n", c[i]);
ss= c[i];
i = n+1;
}
}

return ss;
}


// Fourth function ---------------------the main -------------

int main()
{
printf("\n Input values for y : --> ");
scanf("%f", &y);

printf("\n Input values for t0 (degrees) and E (percentage): --> ");
scanf("%f%f", &to, &E);

newton(&f,to,E);

return 0;
}