Trying to find Velocity and Kinetic Energy

[Rhaen]

The problem is as follows:

A 4.0 kg mess kit sliding on a frictionless surface explodes
into two 2.0 kg parts, one moving at 3.0 m/s, due north, and
the other at 5.0 m/s, 30 degrees north of east. (a) What is
the original speed of the mess kit. (b) How much kinetic
energy was added to the mess kit by the explosion?

I don't know exactly how to get started with this though I know that there would not be any potential energy so we would have the equation:

K_1 = K_2
(1/2)m_1(V^2) = (1/2)m_2(V^2)

But because the explosion adds kinetic energy to the equation through a non-conservative force we would have the equation:

K_1 + W_nc = K_2
(1/2)m_1(V^2) + W_nc = (1/2)m_2(V^2)

Is this correct in my understanding and if so, where would I go from here to get the original velocity? Thank you very much for your time.

-Rhaen-

 

[Hootenanny]

Which quantity is conserved here?

 

[Rhaen]

It would be the left hand side that is conserved which would make:

(1/2)m_1(V^2) = (1/2)m_2(V^2) + W_nc

But what would I do after that if that is the correct equation?

-Rhaen-

 

[Hootenanny]

I was thinking more of momentum.