How Do You Calculate the Initial Speed of a Bullet Using Conservation Laws?

[PnotConserved]

Homework Statement

A bullet of mass (m) is fired into a block of mass (M). The block with the embedded bullet slides across a frictionless table and collides with a horizontal spring whose constant is (k). The springs maximum compression (d) is measured.
Find an expression for the bullets initial speed (Vb) in terms of m, M, k, d.

Homework Equations

mv+Mv=(m+M) V`

1/2mv^2 + 1/2 kd^2 = 1/2 mv^2 +1/2 kd^2

The Attempt at a Solution

I attempted to add the equations together which got me to:
Vb = (m+M)V`
1/2mV`^2 = 1/2 kd^2

...I'm lost

 

[windsupernova]

Well, I think the spring starts in equilibrium so its potential energy is cero.

The block I suppose starts at rest.

I think that you can go from there tbqh

 

[LowlyPion]

You have an inelastic collision. So hopes of simply equating Kinetic energy of the bullet directly to Potential energy in the spring can't be used.

But ... The kinetic Energy of the block can be used.

That depends on its V' which you know from conservation of momentum is:

V' = Vb*m/(M + m)

So yes you do equate just as you have done.

Instead of being lost, you should merely have substituted V' with V' = Vb*m/(M + m) of your first equation and you'd have slept soundly satisfied that you had the right answer.