Two equations, a few unknowns

1. Dec 15, 2013

middlephysics

1. The problem statement, all variables and given/known data

Could someone help me get from these two equations to E'/E=[(A-1)/(A+1)]2

http://postimg.org/image/m5zi9ha19/

2. Relevant equations

E = v^2=E' = v'2 + AV^2
p=v=p' = v' + AV = v

from conservation of energy, momentum

E'/E= (v'2 + AV^2)/(v^2)

3. The attempt at a solution

Three or four pages in my binder with no progress.

2. Dec 15, 2013

Staff: Mentor

$$mv = mv' + AmV$$ can be written as $$mv - mv'= AmV$$ and this gives $$(mv - mv')^2= (Am)^2 V^2$$
You can use this in the equation for the conservation of energy and get rid of V, so just v' and v' are left as unknown, and their ratio is related to E'/E.

3. Dec 15, 2013

middlephysics

Ok from what you wrote I've solved for $$V^2=(mv-mv')^2/(Am)^2$$.

Now I then plugged that V^2 into my $$E'/E= (v'2 + AV^2)/(v^2)$$

I am left with something like

$$(v'(A-1)+v^2-2vv')/(Av^2)$$

so far so good?

4. Dec 15, 2013

middlephysics

I've figured it out, thank you