// **************************
//
//   Project 1: Curling Collision
//   This program computes the effects when a half-size 
//   curling stone collides with a full-size one.  The effects
//   include the momentum shift to the large stone (its angle 
//	 and velocity) and the change in speed of the small stone
//	 (its new velocity).
//	 All velocities are in meters/second.
//
//   Written by Jim Wolfe
//   Due on 17 January 2007
//   Input:  None - initial velocity of small stone and the
//				deflection angle are set as constants
//   Output: Velocity and angle of the large stone and
//				the remaining velocity of the small stone
// **************************

#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

const double ONE_EIGHTY = 180.0;	// Degrees in a radian
const double PI = 3.14159265359;	// Accurate version of Pi
const double INITIAL_VELOCITY = 8.0;	// Starting speed of small
const double SMALL_ANGLE = 40.0;		// Deflection angle of small

double Square (double);				// Function to square a value

int main ()
{
	double		newVelocity;		// Changed velocity of small
	double		bigRockVelocity;	// Velocity of large stone
	double		bigRockAngle;		// Angle of large stone (radians)
	double		bigRockDegrees;		// Angle of large stone (degrees)
	double		cosSmallAngle;		// Cosine of deflection
	double		sinSmallAngle;		// Sine of deflection
	double		sinSquared;			// Sine of deflection squared
	double		cosSquared;			// Cosine of deflection squared
	double		part1;				// Part 1 of formula for angle
									//  large stone takes
	double		part2;				// Part 2 of formula

	cout << fixed << showpoint << setprecision(3);
		// Display initial conditions
	cout << "Initial velocity of " << INITIAL_VELOCITY  << " m/s and deflection of "
		<< SMALL_ANGLE << " degrees" << endl;
		// Convert to radians and get trig function values & squares
	cosSmallAngle = cos (SMALL_ANGLE / ONE_EIGHTY * PI);
	sinSmallAngle = sin (SMALL_ANGLE / ONE_EIGHTY * PI);
	sinSquared = Square(sinSmallAngle);
	cosSquared = Square(cosSmallAngle);
		// Calculate angle large stone takes to small stone path
	part1 = cosSmallAngle * sqrt(3.0 + cosSquared);
	part2 = sqrt((1.0 + cosSquared - part1)/4.0);
	bigRockAngle = asin(part2);
		// Convert to degrees for display
	bigRockDegrees = bigRockAngle * ONE_EIGHTY / PI;
		// Calculate large stone's velocity
	bigRockVelocity = (INITIAL_VELOCITY * part2) / (2.0 * (cosSmallAngle * part2
		+ sinSmallAngle * cos (bigRockAngle)));
		// Calculate small stone's remaining velocity
	newVelocity = 2.0 * bigRockVelocity * part2 / sinSmallAngle;
		// Display results
	cout << endl;
	cout << "New velocity for small rock: " << newVelocity << " m/s" << endl;
	cout << "Big rock velocity: " << bigRockVelocity << " m/s" << endl;
	cout << "Big rock angle: " << bigRockDegrees << " degrees" << endl << endl;;

	return 0;
}

// Square a floating point value

double Square (double arg)		// Value to take square of
{
	return arg * arg;			// Calculate and return result
}