Block hits block with spring. COE and COM

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A 3.0 kg block moving at 8.0 m/s collides with a stationary 4.5 kg block attached to a spring with a spring constant of 720 N/m. The maximum compression of the spring needs to be determined, along with the final velocities of both blocks after the collision and whether the collision is elastic or inelastic. The user attempted to equate spring potential energy with kinetic energy but encountered issues with their calculations. They confirmed the collision is elastic, indicating that both momentum and kinetic energy are conserved. Further clarification and hints from previous discussions are suggested for solving the problem accurately.
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I'm doing the same problem as in this thread: https://www.physicsforums.com/showthread.php?t=70219

Homework Statement


A 3.0 kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hooke's law and has spring constant k = 720 N/m, is attached to the second block in such a way that it will be compressed when struck by the moving block

a. what will be the maximum compression of the spring?
b. what are the final velocities of the blocks after collision?
c. is the collision elastic or inelastic?

Homework Equations



I guessed at c and it's elastic, so both momentum and kinetic energy are conserved

COM: mAv0A=mAvFA+mBvFB

COE:
1/2mAv0A^2=1/2mAvFA^2+1/2mBv)B^2

Potential spring energy= 1/2kx^2

The Attempt at a Solution



a.I tried setting the spring potential energy and kinetic energy of mass A equal, but that doesn't work. I don't really know how to work with springs...
b.I tried solving the system of equations that's in the other thread, but I go something like x=0, so something is wrong there
c.it's elastic. yay =D
 
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