Question

In the equation M1V1+M2V2=M1V1'+M2V2' find the formula for the following:
V1 , V2 , V1' , V2'
Please show/explain how to answer

Answer 1

if these are just given then for example for V1=(M1V1'+M2V2'-M2V2)/M1

Answer 2

You may need another equation probably using the coefficient of restitution.

Answer 3

If v1 and v2 is known, it's easy to find v1' and v2'.
(1/2)m1v1^2+(1/2)m2v2^2=(1/2)m1v1'^2+(1/2)m2v2'^2
m1v1^2+m2v2^2=m1v1'^2+m2v2'^2 ...(1)
m1(v1^2-v1'^2)=m2(v2'^2-v2^2) ...(2)
and the given,
m1v1+m2v2=m1v1'+m2v2' ...(a)
m1v1-m1v1'=m2v2'-m2v2
m1(v1-v1')=m2(v2'-v2) ...(3)
Divide (2) by (3)...
v1+v1'=v2+v2' ...(4)
m2v1+m2v1'=m2v2+m2v2' (multiplying by m2) ...(5)
subtract (5) by (a)...
2m2v2+(m1-m2)v1=(m1+m2)v1'
you can find v1' from here.
In the same way, multiply (4) by m1, then add to (a)...
you can find v2'.