Elastic Collision Formula: Solving for Final Velocity and Mass Ratios

[Puddles]

Homework Statement

An object of mass m1 traveling with velocity v1i has a perfectly elastic collision in which it rear ends and object of mass m2 (m2>>m1) traveling with velocity v2i. How must the velocity v1i relate to v2i if the mass m1 is to stop in its tracks (v1f=0)? What happens if velocity v1i is greater than this? If it is smaller?

Relevant equations
KE = .5mv^2
P = mv

The attempt at a solution
Cons Energy
.5m1v1i^2 + .5m2v2i^2 = .5m2v2f^2

V2f = sq.rt(( m1v1i^2 + m2v2i^2 )/(m2))

Cons Momentum
m1v1i + m2v2i = m2v2f

V2f = ( m1v1i + m2v2i )/(m2)

Set equal to each other, but my answer keeps getting more complex? It's a math error, but I'm not sure what it is…

I get to here:(m1^2v1i^2)+(2m1v1im2v2i)+(m2^2v2i^2) = (m1v1i^2)+(m2v2i^2)

Can anyone help me continue to work this out? I'm frustrated because this is a simple problem but I can't get it.

 

[Puddles]

Okay, I think I found my error, I've worked out that v1i = (m2(1 - 2v2i))/(m1), how can I plug this back into check it? I'm struggling to find a way to do so but I know there must be a way…

 

[haruspex]

Okay, I think I found my error, I've worked out that v1i = (m2(1 - 2v2i))/(m1), how can I plug this back into check it? I'm struggling to find a way to do so but I know there must be a way…

Is there a typo there? 1-velocity is dimensionally invalid.