Conservation of Momentum Problem

[Glorzifen]

Homework Statement

Objects A and C are made of different materials, with different
“springiness,” but they have the same mass and are initially at
rest. When ball B collides with object A, the ball ends up at rest.
When ball B is thrown with the same speed and collides with
object C, the ball rebounds to the left. Compare the velocities of
A and C after the collisions. Is vA greater than, equal to, or less
than vC?

Homework Equations

Pi = Pf

The Attempt at a Solution

A: m_b(V_bi) = mV_Af
B: m_bV_Bi = m_bV_Bf + mv_Cf

Now...I can see that:
V_Af= m_b(V_bi)/m
V_Cf = (m_b(V_bi) - m_bV_Bf )/m

I don't think I can say, from the above equations which is bigger (VAf or VCf)...do I have to sub one into the other now? How do I continue the solution? Thanks for your help!

 

[kuruman]

First off equation B is incorrect. If the ball rebounds to the left, its final velocity should be negative.

Change the sign as indicated above and proceed as you did. Then take the ratio V_Af/V_Cf. Is it greater or less than one?