Speed of object after collision related to spring

[songoku]

Homework Statement

As shown in the figure below, object A (mass: m) is at rest on a smooth, horizontal surface, and a lightweight spring that compress / stretches in the horizontal direction is attached to it. Object B, which has the same mass m, approaches A from the left side with speed v and collides with the spring. The spring compresses and A begins to move. A, B, and the spring travel in a straight line. What is the speed of A when the spring is at maximum compression?

Homework Equations

conservation of energy
momentum?

The Attempt at a Solution

I tried using conservation of energy:

Kinetic energy of B before hitting the spring = elastic potential energy of spring at maximum compression + kinetic energy of A

But then I stuck because I don't know how to change the spring constant and maximum compression to other variables

 

[haruspex]

But then I stuck

so consider

momentum?

Do the conditions for momentum conservation exist here?

 

[songoku]

Do the conditions for momentum conservation exist here?

Yes, taking both boxes and spring as a closed system.

At maximum compression, object A and B will move with same speed?

Using conservation of momentum:
m_Au_A + m_Bu_B = (m_A+m_B) V
V = 1/2 v

Is this correct?

 

[haruspex]

Yes, taking both boxes and spring as a closed system.

At maximum compression, object A and B will move with same speed?

Using conservation of momentum:
m_Au_A + m_Bu_B = (m_A+m_B) V
V = 1/2 v

Is this correct?

That's it.

 

[songoku]

Thanks a lot for the help