Conservation of energy and momentum Problem

[rzn972]

Homework Statement

A 16 kg block is initially at rest on a rough horizontal surface (uk= .2). The block has a small explosive charge inside it. The charge explodes, splinting the block into two fragments and adding 76.8 joules of kinetic energy. The other 10kg slides 1.47m along the rough surface before coming to Rest. How far does the other 6kg fragment slide along the rough surface before it comes to rest?
Must be solved using conservation laws.

Homework Equations

The Attempt at a Solution

Using conservation of momentum:
6va = 10vb
vb= .6 va
line 1: 76.8 = .5 * 6 *va^2 + .5* 10 * vb^2
va = 4
line 2: .5 * 6 * 4^2 + -.2 * 6 * g * da= 0
da= 4.08
I am not sure where the equation from line 1 and 2 came from.
Is line 1 using work = change in kinetic energy?
I am not sure what equation is used for line 2.

 

[dauto]

line 1 computes total kinetic energy after explosion
line 2 uses the work of friction force and sets it equal to the change in kinetic energy