Finding least time for object to roll on graph

using System;
using System.Diagnostics;
using System.Threading;
using System.Globalization;

class Program
{

    static void Main()
    {
        int version = 1;
        string type = "parabola";
        double gravitationalA = 9.81d;
        double[] startPoint = { 80, 20 };
        double[] endpoint = { 0, 0 };
        Boolean calculateDistance = true;

        Console.WriteLine("Following Variables are used:");
        Console.WriteLine("Gravitational Accel: " + gravitationalA + " m/s");
        Console.WriteLine("Goal: " + endpoint[0] + "," + endpoint[1]);
        Console.WriteLine("Start: " + startPoint[0] + "," + startPoint[1]);
        Console.WriteLine("Calculate Distance" + calculateDistance);
        Console.WriteLine("y/n");
        string confirmation = Console.ReadLine();

        if (confirmation != "y")
        {
            Console.WriteLine("");
            Console.WriteLine("Abort, Please change the variable");
            Console.WriteLine("graph type");
            type = Console.ReadLine();
            Console.WriteLine("Gravitational Acceleration");
            gravitationalA = double.Parse(Console.ReadLine(), CultureInfo.InvariantCulture.NumberFormat);
            Console.WriteLine("Start Point X");
            startPoint[0] = double.Parse(Console.ReadLine(), CultureInfo.InvariantCulture.NumberFormat);
            Console.WriteLine("Start Point Y");
            startPoint[1] = double.Parse(Console.ReadLine(), CultureInfo.InvariantCulture.NumberFormat);
            Console.WriteLine("");
            Console.WriteLine("Following Variables are used:");
            Console.WriteLine("Gravitational Accel: " + gravitationalA + " m/s");
            Console.WriteLine("Goal: " + endpoint[0] + "," + endpoint[1]);
            Console.WriteLine("Start: " + startPoint[0] + "," + startPoint[1]);
            Thread.Sleep(3000);
        }

        Stopwatch stopwatch = new Stopwatch();
        stopwatch.Start();
        Console.WriteLine("");
        Console.WriteLine("Starting calculation");
        double x = startPoint[0];
        double velX = 0f;
        double timestep = 0.0001f;
        double time = 0f;
        double initialCollvar = 1;
        double initialCollvarStep = 0.1f;
        double zeroInAccuracy = 0.0001f;
        double maxTime = double.PositiveInfinity;
        double limit = 400;
        string strg = "";
        Console.WriteLine(limit);
        Tuple<double, double> calculateAcceleration(double X, double collVar, double depvar1, double depvar2)
        {
            double localSlope = 2.0f * collVar * (X - depvar1);

            //return -(float)(Math.Cos(Math.Atan(1f / localSlope)) * Math.Sin(Math.Atan(1f / localSlope)) * gravitationalA);
            return Tuple.Create(-(double)(Math.Cos(Math.Atan(1f / localSlope)) * Math.Sin(Math.Atan(1f / localSlope)) * gravitationalA), localSlope);
        }
        Tuple<double, double> calculateAccelerationCircle(double X,double Y, double collVar, double h, double k)
        {
            double localSlope = (h-X)/(Y-k);

            //return -(float)(Math.Cos(Math.Atan(1f / localSlope)) * Math.Sin(Math.Atan(1f / localSlope)) * gravitationalA);
            return Tuple.Create(-(double)(Math.Cos(Math.Atan(1f / localSlope)) * Math.Sin(Math.Atan(1f / localSlope)) * gravitationalA), localSlope);
        }

        Console.WriteLine(strg);
        Console.WriteLine("");
        strg = "";
        Tuple < double,double ,double, double> CalculateTimeParabola(double initialCollvar)
        {
            double h = 0;
            double k = 0;
            double distance = 0;
            double deltaX = 0;

            x = startPoint[0];
            velX = 0f;
            time = 0f;
            distance = 0f;
            h = 0.5f * (startPoint[0] - (startPoint[1] / (startPoint[0] * initialCollvar)));
            k = -initialCollvar * (double)Math.Pow(h, 2);
            while (x >= 0 && time < limit)
            {
                Tuple<double, double> calculatedVales = calculateAcceleration(x, initialCollvar, h, k);
                deltaX = (double)(velX * timestep + 0.5f * calculatedVales.Item1 * Math.Pow(timestep, 2));
                x = (double)(x + deltaX);
                velX = velX + (0 + calculateAcceleration(x, initialCollvar, h, k).Item1) * timestep / 1f;
                distance = distance + (double)Math.Sqrt(deltaX * deltaX * (calculatedVales.Item2 * calculatedVales.Item2 + 1.0f));
                time = time + timestep;
            }

            return Tuple.Create(time, initialCollvar, h, k);
        }

        Tuple<double, double, double, double> CalculateTimeCircle(double initialCollvar)
        {
            if (initialCollvar < (double)Math.Sqrt(Math.Pow(startPoint[1], 2) + Math.Pow((Math.Pow(startPoint[1], 2) - Math.Pow(startPoint[0], 2)) / (-2 * startPoint[0]), 2)))
            {
                return Tuple.Create(limit, initialCollvar, 0.0d, 0.0d);
            }
            double q = Math.Sqrt(Math.Pow(startPoint[1],2) + Math.Pow(startPoint[0],2));
            double x3 = startPoint[0] / 2;
            double y3 = startPoint[1] / 2;


            double h = x3 + (Math.Sqrt(Math.Pow(initialCollvar,2)-Math.Pow(q/2,2))*(-startPoint[1]))/ q;
            double k = y3 + (Math.Sqrt(Math.Pow(initialCollvar,2)-Math.Pow(q/2,2))*(startPoint[0])) / q;

            double distance = 0;
            double deltaX = 0;

            x = startPoint[0];
            velX = 0f;
            time = 0f;
            distance = 0f;
            double y = k - Math.Sqrt(Math.Pow(initialCollvar, 2) - Math.Pow(x - h, 2));
            while (x >= 0 && time < limit)
            {
                y = k - Math.Sqrt(Math.Pow(initialCollvar, 2) - Math.Pow(x - h, 2));
                Tuple<double, double> calculatedVales = calculateAccelerationCircle(x,y, initialCollvar, h, k);
                deltaX = (double)(velX * timestep + 0.5f * calculatedVales.Item1 * Math.Pow(timestep, 2));
                x = (double)(x + deltaX);
                velX = velX + (0 + calculateAccelerationCircle(x,y, initialCollvar, h, k).Item1) * timestep / 1f;
                distance = distance + (double)Math.Sqrt(deltaX * deltaX * (calculatedVales.Item2 * calculatedVales.Item2 + 1.0f));
                time = time + timestep;
            }

            return Tuple.Create(time, initialCollvar, h, k);
        }

        Tuple<double, double, double, double, double, double> jumpingDecend()
        {
            //   Console.WriteLine(Math.Abs(initialCollvarStep)+","+zeroInAccuracy);
            double var1=0;
            double var2=0;
            double var3 = 0;
            double var4 = 0;
            if (type == "parabola")
            {
                var1 = 0;
                var2 = 0;
            }
            if (type == "circle")
            {
                initialCollvar = (double)Math.Sqrt(Math.Pow(startPoint[1], 2) + Math.Pow((Math.Pow(startPoint[1], 2) - Math.Pow(startPoint[0], 2)) / (-2 * startPoint[0]), 2));
                Console.Write(initialCollvar);
            }

            while (Math.Abs(initialCollvarStep) >= zeroInAccuracy)
            {
                // --  Console.Write("BOB");
                initialCollvar = initialCollvar + initialCollvarStep;
                if (type == "parabola")
                {
                    time = CalculateTimeParabola(initialCollvar).Item1;
                }
                else if (type == "circle")
                {
                    time = CalculateTimeCircle(initialCollvar).Item1;
                }
                // Console.WriteLine(distance);
                //  Console.WriteLine(initialCollvar + "(x-" + h + ")^2+" + k);
                strg = strg + "(" + initialCollvar + "," + time + ")" + ",";
                if (maxTime > time)
                {
                    maxTime = time;
                    initialCollvarStep = initialCollvarStep * 2;
                }

                else if (time > maxTime)
                {
                    if (time >= limit)
                    {
                        initialCollvar = initialCollvar - initialCollvarStep;
                        initialCollvarStep = -initialCollvarStep / 4;
                    }
                    else
                    {
                        initialCollvarStep = -initialCollvarStep;
                    }
                }
                else
                {
                    initialCollvarStep = initialCollvarStep / 2;
                }
            }
            if (type == "circle")
            {
                Tuple<double, double, double, double> resultcal = CalculateTimeCircle(initialCollvar);
                time = CalculateTimeCircle(initialCollvar).Item1;
                var1 = resultcal.Item1;
                var2 = resultcal.Item3;
                var3 = resultcal.Item4;
            }
            else if (type == "parabola")
            {
                Tuple<double, double, double, double> resultcal = CalculateTimeParabola(initialCollvar);
                time = CalculateTimeParabola(initialCollvar).Item1;
                var1 = resultcal.Item2;
                var2 = resultcal.Item3;
                var3 = resultcal.Item4;
            }
            if (time > limit)
            {

                if (type == "circle")
                {
                    initialCollvar = initialCollvar - initialCollvarStep / 2;
                    Tuple<double, double, double, double> resultcal = CalculateTimeCircle(initialCollvar);
                    time = resultcal.Item1;
                    var1 = resultcal.Item2;
                    var2 = resultcal.Item3;
                    var3 = resultcal.Item4;
                }
                else if (type == "parabola")
                {
                    initialCollvar = initialCollvar - initialCollvarStep / 2;
                    Tuple<double, double, double, double> resultcal = CalculateTimeParabola(initialCollvar);
                    time = CalculateTimeCircle(initialCollvar).Item1;
                    var1 = resultcal.Item2;
                    var2 = resultcal.Item3;
                    var3 = resultcal.Item4;
                }
            }
            Console.WriteLine("Finished");
            return Tuple.Create(initialCollvar, time, var1,var2,var3,var4);
        }
        Tuple<double, double, double, double, double, double> resultTuple = jumpingDecend();
        Console.WriteLine("");
        Console.WriteLine("time taken " + resultTuple.Item2 + " seconds");
        Console.WriteLine("At variable = " + resultTuple.Item1);
        Console.WriteLine("h = " + resultTuple.Item4);
        Console.WriteLine("k = " + resultTuple.Item5);
        Console.WriteLine();
        stopwatch.Stop();
        Console.WriteLine("");
        Console.WriteLine("Calculation Time is {0} s", stopwatch.ElapsedMilliseconds / 1000f);
        Console.WriteLine("Closing In 10 seconds");
        Console.WriteLine(strg);
        Thread.Sleep(10000);
    }
}