重力場中（空気抵抗あり）の物体のx-tグラフのための数値計算

#include < stdio.h >
main()
{
double t, x, dt, dx, ta, tb, v;
double f(double ,double );
int i, n;
x = 0.0 ;
t = 0.0 ;
ta = 0.0 ;
tb = 100 ;
v = 0.0 ;
n = 1000;
dt = (tb - ta) / n ;
for ( i = 0; i < n ; i++){
x = x+ v*dt ;
v = v+ f(v, t)*dt ;
t = t + dt ;
printf(" %e %e \n", t, x);
}
}
double f( double x, double t){
double y, z, alpha, g;
alpha = 0.1;
g = - 9.8;
z = -alpha * x + g ;
return z;
}