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**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.

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.