How do you solve this Pool Game?

Question

I know the answer is B, but I am unclear as to why it is. If someone could kindly explain the process of finding the answer or possibly show a simulation, it would be awesome.

Thank You.

Answer 1

You can follow the ball path across the table. The point that makes that easy is that the ball starts in a direction of 45°. Thus, all collision angles will be 45°. Therefore, you have to invert only one component of the ball's direction vector.

Here is some C# sample code. The coordinate system's origin is at the bottom left corner of the table. The ball position is measured at its bounding box' bottom left corner:

int ballX = 0;
int ballY = 0;
int ballWidth = 5;
int tableWidth = 230;
int tableHeight = 130;

int directionX = 1;
int directionY = 1;

while(true)
{
    //the distances that the ball could travel until it collides with a vertical or horizontal border, respectively
    int travelDistanceX, travelDistanceY;
    if (directionX > 0)
        travelDistanceX = tableWidth - ballWidth - ballX;
    else
        travelDistanceX = ballX;

    if (directionY > 0)
        travelDistanceY = tableHeight - ballWidth - ballY;
    else
        travelDistanceY = ballY;

    if(travelDistanceX == travelDistanceY)
    {
        //we found the target pocket:
        Console.WriteLine("Target is located at {0}/{1}.", ballX + travelDistanceX * directionX, ballY + travelDistanceY * directionY);
        break;
    }

    if(travelDistanceX < travelDistanceY)
    {
        //collision with the vertical borders
        ballX += travelDistanceX * directionX;
        ballY += travelDistanceX * directionY;
        directionX *= -1;
    }
    else
    {
        //collision with the horizontal borders
        ballX += travelDistanceY * directionX;
        ballY += travelDistanceY * directionY;
        directionY *= -1;
    }
    Console.WriteLine("Collision at {0}/{1}.", ballX, ballY);
}

The code results in the following path:

Collision at 125/125.
Collision at 225/25.
Collision at 200/0.
Collision at 75/125.
Collision at 0/50.
Collision at 50/0.
Collision at 175/125.
Collision at 225/75.
Collision at 150/0.
Collision at 25/125.
Collision at 0/100.
Collision at 100/0.
Target is located at 225/125.

And the pocket at (225/125) (add the ball width to get the actual position) is B.