Think about this plot based on the region. The area on the graph containing the blue data (hitting the 2nd ball) is much larger than the area on the graph that shows the speed required to hit the ball. It arrives information very difficult to achieve a hit that affects all four balls.

Let’s do one more. What if I add 4 balls to the collision list?

To put it bluntly, this is a comparison of the speed of the starting ball which causes the ball 3 to hit four balls. Let me cross the rough lines to restart the running ball.

To make a single ball hitting a 2 ball, the speed of x can be from about 0 m / s to 1 m / s. (I did not calculate speeds exceeding 1 m / s.) These speeds can range from approximately 0.02 to 0.18 m / s. It has an x ​​speed of 1 m / s and a y-speed of about 0.16 m / s.

For the 2nd ball to hit the 3rd ball, the speed of x can be from 0.39 to 1 m / s and y-speed from 0.07 to 0.15 m / s. Note that the x speed has dropped to 0.61 m / s and the y-speed is now 0.08 m / s.

Finally, for the 3rd ball to hit the 4th ball, the speed of x can be from 0.42 to 1 m / s and y-speed from 0.08 to 0.14 m / s. This gives an x-rent of 0.58 m / s with a y-range of 0.06 m / s.

I think you can see what’s going on: More collisions mean fewer bumps that can hit the last ball.

Now we have to try the final case: nine balls. Here is what it looks like:

Well, that works. But would the last ball still hit if we had more gravitational pull because of the connection between the cue ball and the player?

This is easy to try. All I have to do is add another character. I will use almost a round man. I know, people are not round. But if you want to calculate gravity for a real player, you have to calculate the hardest. Each part of the person has a different mass and can be a different distance (and way) from the ball. But if we assume that the person is a spider, then it would be the same as if the whole mass was based on a single point. These and calculations we can do. And in the end, the difference in gravity between the real person and the real person may not be so important.