Conservation of momentum with sprins

[Matt_h]

Homework Statement

Problem 2 (35 points): A projectile of mass mA=20g is shot towards a block of mass
MB= 5kg with a velocity of vA=400m/s. The block is at rest, attached to a horizontal
massless spring (at equilibrium) with k=500N/m.

a. If the collision between the projectile and the mass is perfectly elastic,
what are the velocities of the two masses immediately following the collision?

Homework Equations

U(x)=1/2kx^2
F=ma
Conservation of momentum
M1U1 + M2U2 = M1V1 + M2V2
When U is equal to the velocity before the impact.

The Attempt at a Solution

I would have a good idea on how to do this problem without the spring being there but with it there i can not figure out how to do it.

I know that the total velocities after the collision needs to combine to make 400 but other than that i am pretty lost on this one.

 

[haruspex]

The spring is there to confuse you. Immediately after impact, how far has the spring compressed? What, then, is the force in it?