To what depth will the bullet penetrate the block in this case?

[yb1013]

Homework Statement

A 7.00 g bullet, when fired from a gun into a 1.00 kg block of wood held in a vise, penetrates the block to a depth of 7.40 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

p= mv
p1i + p2i = p1f + p2f
and probably some other equations.. not really sure

The Attempt at a Solution

ok well I would really appreciate it if someone could please kind of walk me through this problem, I'm not trying to get anyone to do my homework. In fact I already have the answer which is 7.35 cm but i really have no idea how to get it. I've read up on some previous posts about this question and I still just can't figure it out.

I know it has something to do with conserving momentum and then turning that into conserving kinetic energy which will find the speed? Some thing like that, but could someone please kind of lay the format out, because i have a test tmw on this and I could really use some help.

Thank you!

 

[Astronuc]

In the first case, the wood block is fixed and all the bullets energy goes into penetrating the block of wood, or the block decelerates the bullet. If one assumes constant acceleration (constant force), one can determine the force of the block on the bullet.

In the second case, the block is free to move so some of the initial kinetic energy of the bullet is transformed to kinetic energy of the block which accelerates while the bullet is decelerating.

 

[yb1013]

im trying to understand, but i just have like this mental block on this problem. Out of all the questions in my test review there's really only two that i don't understand, and this is one of them.

like what formula could you use for the first part with the vise?