Inelastic collision: finding initial velocity of projectile

[phys1618]

Homework Statement

One way to measure the muzzle velocity of a bullet is to fire it horizontally inot a massive block of wood hanging from a string an d measure the height to which the wood (containing the bullet) rises.
in one experiment the bullet had a mass of .05kg, and the wood has a mass of 2kg. After the shot, the wood and bullet rose to a height of .5 meteres. what was the original speed of the bullet?

Homework Equations

d=(vf2-vi2)/2a
KE=1/2Mv2
change of ENERGYsystem=constant
PEi +KEi=PEf + KEf
PE=Mgh

The Attempt at a Solution

i ended up with 29.17 m/s for the original speed

 

[phyzmatix]

Could you show your work please?