Conservation of Momentum- Elastic collision

[MostlyHarmless]

Homework Statement

A small ball of mass, $m_1$ is aligned above a larger ball of mass $m_2=0.63kg$, with a slight separation. The two are dropped simultaneously from a height $h=1.8m$(Assume the radius of each ball is negligible relative to h.) (a) If the larger ball rebounds elastically from the floor and then the small ball rebounds elastically from the larger ball, what value of $m_1$ results in the larger ball stopping when it collides with the small ball?(b)What height does the small ball then reach?

Homework Equations

$p=mv$
$KE=(1/2)mv^2$
For part b: $v^2_f=v^2_i+2a(y-y_0)$

The Attempt at a Solution

I used $PE=KE$ to find the velocities of both balls as they reach the ground to be $v_1=v_2=5.9m/s$. Where v1 is the velocity of the larger ball and v2 is of the smaller ball.
Since the big ball rebounds elastically off the floor and the floor doesn't move, it's velocity after bouncing is just $v_1=-5.9m/s$.
Other values deduced: $v_1'=0$, where $v_1'$ is the velocity AFTER colliding with the ball.

$m_1v_1+m_2v_2=m_1v_1'+m_2v_2'$ Where $v_2'$ is the velocity of the small ball after the collision with the larger ball. $m_1v_1'=0$ if the large ball stops.

Where I'm getting hung up is I have 2 unknowns. I tried also writing out the an equation depicting conservation of KE and using those two as a system of equations, but I'm either doing my algebra wrong, or it's just not the right way to go. I have what I think is a clear pictured of what is going on in my head, but I'm just not seeing how to get mass without that other velocity$v_2'$. The answer in the back of the book is .21kg. I'm not worried about part b. That part will be easy enough after I finish part a.

 

[haruspex]

Where v1 is the velocity of the larger ball and v2 is of the smaller ball.

You have your 1s and 2s swapped. m₁ is the smaller ball.

I tried also writing out the an equation depicting conservation of KE and using those two as a system of equations, but I'm either doing my algebra wrong, or it's just not the right way to go.

It is the right way to go. You are told the balls bounce elastically off each other, and you need this extra equation. Pls post your working.