Solving the Billard Ball Rebound Problem

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    Ball Calculus
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Homework Help Overview

The discussion revolves around a project involving billiard balls on a table, specifically determining the direction from which a first ball should be struck so that it rebounds off the table's edge and impacts a second ball. The problem assumes elastic reflection at the table's edge and involves both analytical and geometric expressions, particularly for a circular table.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the angle of incidence equating to the angle of reflection and the need to express the problem analytically and geometrically. There are questions about the assumptions regarding the positions of the balls and how to derive the necessary formulas. Some suggest placing the table in a coordinate system to facilitate calculations.

Discussion Status

The discussion is active, with participants exploring various interpretations of the problem. Some have offered guidance on setting up the problem in a coordinate system and working through the algebra, while others express uncertainty about deriving the formulas needed. There is no explicit consensus on a single approach, but multiple lines of reasoning are being examined.

Contextual Notes

Participants mention the potential need to consider all edges of the table versus just one, depending on the project requirements. There is also a focus on the implications of using a circular table and how that affects the calculations.

htrimm08
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I have a project to do on billard balls, just one problem, I have no idea how to start it off.. I was wondering if anybody had an idea about it?

"given a billard table, and two balls on it, from which direction should the first ball be struck, so that it rebounds off the rim of the table and then impacts the second ball?

we will assume that the ball reflects elastically at the billard, ie the table edge.
 
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Use the angle of incidence = angle of reflection. But surely you have more information. There will be several correct answers in general.
 
yeah, I've gotten that far, asumed the points of the two balls...we have to express this analytically and geometrically, I have no idea how to come up with the formula of this... we also have to use a circular table as well and compare them
 
htrimm08 said:
yeah, I've gotten that far, asumed the points of the two balls...we have to express this analytically and geometrically, I have no idea how to come up with the formula of this... we also have to use a circular table as well and compare them

I guess you will just have to bite the bullet and slug your way through it. Put the table in the first quadrant with one ball at (a,b) and the other at (c,d) and work out the algebra. Dunno if you can do just one rail or have to do all four; depends on what your teacher wants. Once you've done one the others should be easy. :-p
 
Is it ok to assume the points of the balls, say if it was on a graph? and then with that find the angle of the point of incidence? I am still stumped as to how to find the formula after this... anyone willing to do it for me? lol. jk
 
LCKurtz said:
I guess you will just have to bite the bullet and slug your way through it. Put the table in the first quadrant with one ball at (a,b) and the other at (c,d) and work out the algebra. Dunno if you can do just one rail or have to do all four; depends on what your teacher wants. Once you've done one the others should be easy. :-p

htrimm08 said:
Is it ok to assume the points of the balls, say if it was on a graph? and then with that find the angle of the point of incidence? I am still stumped as to how to find the formula after this... anyone willing to do it for me? lol. jk

Let the rail you use be the x-axis so the bounce point is (p,0). Then work with the slopes of the lines from the balls to the point to figure out p for equal angles.
 
If the table is circular then set the normal line for angle of incidence perpendicular to the tangent line at point of impact.
 

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