Deriving the head-on collision equation in terms of v2' and v1'

[louise82]

[SOLVED] Deriving the head-on collision equation in terms of v2' and v1'

I think I'm having an algebra issue here, but how is the momentum equation (where v2=0):

m1(v1-v1')=m2v2'

combined with v1+v1'=v2'

to give:

v2' = v1 [ 2m1/(m1+m2)]

and

v1' = v1 [(m1-m2)/(m1+m2)]


I'm realizing this must be an elementary question since my book doesn't actually show how they derive those equations, but I'm not seeing it.

Help someone?

 

[quantumdude]

Plug v2'=v1+v1' into the first equation, and then solve for v1'.

 

[Hurkyl]

So... you have two equations... and you are trying to eliminate one of the variables?

 

[louise82]

Ok, I can find v1', but I'm confused on which equation to plug in where to get v2'.

 

[quantumdude]

They gave you v2' in terms of v1 and v1', did they not?

 

[Hurkyl]

Ok, I can find v1', but I'm confused on which equation to plug in where to get v2'.

There aren't very many options... why not try them all?

 

[louise82]

Ok, feel dumb now. But since I'm exposed I may as well ask all my other dumb questions. Thanks for the help. :)

 

[quantumdude]

Ok, feel dumb now. But since I'm exposed I may as well ask all my other dumb questions. Thanks for the help. :)

Hey louise, you got it, so you should feel smart.