Solving the Billard Ball Rebound Problem

[htrimm08]

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.

 

[LCKurtz]

Use the angle of incidence = angle of reflection. But surely you have more information. There will be several correct answers in general.

 

[htrimm08]

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

 

[LCKurtz]

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.

 

[htrimm08]

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]

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.

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.

 

[zcd]

If the table is circular then set the normal line for angle of incidence perpendicular to the tangent line at point of impact.