Bullet hitting a wood block in a vise. Find initial velocity?

[hevans1]

Homework Statement

A 7.00 g bullet, when fired from a gun into a 1.10 kg block of wood held in a vise, penetrates the block to a depth of 6.40 cm. This block of wood is next placed on a frictionless horizontal surface, and a second 7.00 g bullet is fired from the gun into the block. To what depth will the bullet penetrate the block in this case?

Homework Equations

vf^2 = vi^2 + 2ad
p = mv
m1v1i + m2v2i = (m1+m2)vf
Δp = ƩF dt

The Attempt at a Solution

Honestly, I'm pretty baffled. I can't do anything with momentum without an initial velocity, and I can't find that without acceleration or time. I've seen some other posts that talk about resistive force, but we haven't discussed that so I don't think that's necessary. I think the vise is what's throwing me for a loop. It's inelastic, so there no conserved energy. I'm just not sure what the first step is.

 

[Simon Bridge]

It's a comparison between the vise and the free block.
This is one of those situations where you have to write down a bunch of simultanious equations.

You know that momentum is conserved.

You know the relationship between kinetic energy and momentum.

You know the relationship between work and change in energy, also work and force.

You also know a bunch of kinematic equations and Newtons laws.