How Is Kinetic Energy Distributed in an Explosion with Unequal Mass Fragments?

[ArmandoC]

Homework Statement

An explosion breaks an object into two pieces, one of which has 1.5 times the mass of the other. If 7400 J were released in the explosion, how much kinetic energy did each piece acquire?

Homework Equations

Momentum?
Kinetic Energy?

The Attempt at a Solution

I used all types of formulas having to do with energies and momentum and nothing gave me an answer.

 

[chaoseverlasting]

Use conservation of linear momentum along the horizontal since all the forces are internal (the energy that the explosion released was stored inside the projectile/object).

You know that m1v1+m2v2=0. And are given that m1=1.5m2.
Also, the total energy released in the explosion is converted into kinetic energy (you have to assume that), so $$0.5m_1v_1^2+ 0.5m_2v_2^2=7500$$. Solve for v1/v2 and find the KE of each piece.