# Simple 2D collision formula developments

1. Apr 9, 2009

Hi everybody,
I am currently working on a small computer programming project, and was wondering if you could give me hand.

Say I have two simple, identical balls moving in different speeds and angles towards each other. They hit each other elastically, and weigh exactly the same.
The location of their centers is also a given (see diagram for further explanation).

http://img12.imageshack.us/img12/1108/question.png [Broken]

All the data is according to the diagram (which is completely general).
Can I tell through some sort of formula developments what their new speeds (size+angle) will be, after they collide? (As in U1=?, U2=?, newA1=?, newA2=?)

I tried figuring it out myself but got mixed-up and lost. Hopefully you might be able to help me :-)

Thanks a lot,

Last edited by a moderator: May 4, 2017
2. Apr 9, 2009

### Born2bwire

Oh sure. I actually had to do this myself for a computer game we made for a class project. I don't know the equations but you can get a simple closed form expression for it. I'm sure if you do enough searching on the web or through textbooks you will find out what it is. Of course in the end you could always derive it.

3. Apr 9, 2009

Yeah, I figured it was rather simple, but I can't seem to find anything of that sort anywhere.
A closed form expression would be fantastic, but I am having a hard time deriving it myself. Thus, I turned to you guys for assistance :)
So, can any of you give me a hand?

4. Apr 9, 2009

### Count Iblis

Transform to the center of mass frame in which the total momentum is zero. Forget about the angles and velocities in the original frame for the moment. Just work out the most general case of a collision as seen in the center of mass frame (which is very simple).

Then transform this to a frame in which the initial velocities are arbitrary. You need to do a little algebra to find the angles in that other frame.

5. Apr 9, 2009