help please

A 2.0-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 Hook's law and has spring constant k = 850 N/m, is attached to the second block in such a way that it will be compressed when struck by the moving block. (the picture is a box on the left side with a velocity to the right, which is 8m/s. On the right side is box with a mass of 4.5 kg and a spring attached)

a. What will be the maximum compression of the spring?

b. What will be the final velocities of the blocks after the collision?

The trick is to recognize that the problem is an elastic collision, and so solve part b first. From this you will know the kinetic energy imparted to the second block E=mv^2/2, which you can relate to the energy in the coiled spring via the equation E=kx^2/2.

Actually what I said previously assumed negligible movement of the second mass until the moment of maximum compression, but it actually starts accelerating before that. The real secret is to consider that at maximum compression both masses are moving at the same velocity, which can be calculated using the momentum. Using this velocity, the kinetic energy of the two masses moving together can be compared to the original kinetic energy of the first mass, and the difference will be the potential energy stored in the maximally compressed spring, which will then lead you to the distance of the compression using E=kx^2/2. This gives the anwer to part a. I still maintain that part b can be solved using basic knowledge of fully elastic collisions without needing to solve part a first.