Solving for Unknowns in Conservation of Energy and Momentum Equations

[middlephysics]

Homework Statement

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

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

Homework 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)

The Attempt at a Solution

Three or four pages in my binder with no progress.

 

[mfb]

$$mv = mv' + AmV$$ 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.

 

[middlephysics]

$$mv = mv' + AmV$$ 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.

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?

 

[middlephysics]

$$mv = mv' + AmV$$ 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.

I've figured it out, thank you