// trajectory of projectile with drag
// 
#include<iostream>
#include<cmath>
using namespace std;

int main()
{
	const double dt = .01; 		// time increments
	const double D  = .00126;	// drag coefficient
	const double G  = 9.8;		// gravity
	const double V0 = 500;		// initial velocity

	double angle;
	cout << " Enter an angle " << endl;
	cin >> angle;

	double x=0, y=0;
	double vx = V0 * cos(angle *(M_PI / 180));
	double vy = V0 * sin(angle *(M_PI / 180));
	double xsave, ysave;
		
	while (y>=0)
	{
		double vtotal = sqrt((vx * vx) + (vy * vy));
		xsave = x; ysave = y;
	
		x  = x  + dt * (vx);
		y  = y  + dt * (vy);
		vx = vx + dt * (-D * vx * vtotal);
		vy = vy + dt * (-D * vy * vtotal -G);

		cout << x << " " << y << endl;
	}
	//   note that the final point has y < 0
	//   to get the precise point where y=0, can do
	//   a simple interpolation step as follows:
	//double xfinal = x - y*(xsave-x)/(ysave-y);
	//cout << " projectile distance = " << xfinal << endl;
}