How Do You Calculate the Initial Velocity of a Bullet in an Elastic Collision?

[spectravoid]

Homework Statement

A bullet of mass m is shot into a block of mass M that rests on a rough surface with coefficient of kinetic friction k. The block slides for a distance of x meters before coming to a stop. Derive an expression for the initial velocity of the bullet.

Homework Equations

0.5mvi^2 - k(-1)x = 0.5(M+m)vf^2 (work energy theorem just with the variables replaced with the ones in the question)
and also this but I'm not sure where to use it Ff = (M + m)gk

The Attempt at a Solution

vi = +/- sqrt((vf^2 + (Mvf^2)/m + (2kx)/m))

I need to remove vf

thank you for help

 

[Dick]

You don't want to use the work/energy stuff here. This is an INelastic collision. When the bullet collides with the block it is stopped by friction within the block and you have no data to calculate that directly. What you can count on is conservation of momentum. The initial momentum of the bullet is equal to the initial momentum of the bullet plus block combination. This will let you get an initial velocity for the block. Go from there.