What is the formula of getting the colliding Points x,y

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dhea

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Simulation Scenario:
I have 700x500 size of a rectangle

The first angle of the ball when bouncing the edge of the rectangle is 40degrees.
Starting position of the ball is:
Px = 450
Py = 350

Assuming there is no friction or gravity as I just want to simulate the path of the ball.
What are the points when the ball reaches to the wall as it bounces 5x of the rectangle?

How to get the reflection points that are located at the sides of the table?

Thank you.
 

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It isn't clear how you are measuring angles, or what your coordinate system is (where the origin is). And the picture's angles are totally wrong for actual reflections.

But one way to deal with reflections/bounces on a rectangular "pool table" is to make an infinite grid of reflections of the table itself, so that the path of the ball can be thought of as a straight line. Each time this line crosses a vertical or horizontal line representing a reflection of the table, it has bounced.

See the pictures here.
 
The drawing might not be correct but my idea is I want to know the coordinates of a point when a line reaches at the edge of the rectangle or table and it bounces back with the same angle. This require no Friction as this is just to generate path. Maybe up to 4-5 bounding points.

Any idea to come up with this is very much welcome.

Thank you so much.
 
That page was the help I gave you. Have you tried doing anything with that idea? I'll want to see what you can do with it, and where you need help.

Also, I suspect you haven't told us the entire assignment and context of your question. Please show us whatever you were given.
 
In my heading title "What is the formula of getting the colliding Points x,y". I am asking help on what is the formula of getting the series of points when the ball bounces to the edge of the table.
 
It will not be a single formula. How could one formula give a series of points? And even for one point, it will be an algorithm, as there are four walls to bounce off of, and the result will be different for each.

Please, again, state the entire assignment as given to you (or, if not an assignment, what the context is). In the question, it looked like you just wanted five ordered pairs, which you can find one by one using some trig. The mentions of "formula" and "simulation" suggested you might want something bigger, perhaps a program that would find each point in turn. But you've shown nothing to indicate what you know, what you've tried, and where you are stuck.

In order to help, we need to see what you have tried, and where you need help. Please go back and read our guidelines, which exist so we can offer the most effective help:

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if it is not a single formula, then why not start with a single formula using a Trigonometry to find X or Y using Tan or Cos?
By the way, I measure angle by Kilometer because my billiard table is a big as Pacific Ocean.
 
dhea said:
if it is not a single formula, then why not start with a single formula using a Trigonometry to find X or Y using Tan or Cos?
By the way, I measure angle by Kilometer because my billiard table is a big as Pacific Ocean.
Click to expand...

Yes, please start there, so I can see how much help you will need.

Before I can offer help, or even tell you whether you are right, I need to know answers to the things I mentioned in my first post: "It isn't clear how you are measuring angles, or what your coordinate system is (where the origin is)." I can suppose the origin is at lower left, so the upper right corner is at coordinates (700, 500), I think, and you are starting at (450, 350). But what does "The first angle of the ball when bouncing the edge of the rectangle is 40degrees" mean? Am I to assume the initial path is ENE as in the drawing? Is the 40 degrees measured from the wall, or from the normal (perpendicular) to the wall? That is, is the ball moving at an angle 40 degrees from north, or 40 degrees from east?

Once you define that clearly, you can draw a right triangle with base 250 and a known angle, so basic trig will give you the rise along the eastern side of the rectangle. If that turns out to be past the top of that side, you'll have to make a different triangle to find the location along the top.

But I have to add, if you are really talking about the width of the Pacific, then you are not "playing" on a plane surface, and everything changes. Your coordinates would have to be latitude and longitude, and you'll need spherical trigonometry. Luckily, 700 by 500 km is far smaller than the Pacific; but it would still require spherical trig.
 
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