Solve Linear Momentum: An Explosion Problem and Find the Answer

[pupatel]

Here's another one that it giving me a lot of trouble...althought it looks easy, i have tried eveything i could to solve it...but still doesn't give me the right answer...

An explosion breaks an object into two pieces, one of which has 1.5 times the mass of the other. if 7500 J were released in the explosion, how much kinetic energy did each piece acquire?

How do i solve this and what is the answer?

 

[AKG]

Here's another one that it giving me a lot of trouble...althought it looks easy, i have tried eveything i could to solve it...but still doesn't give me the right answer...

An explosion breaks an object into two pieces, one of which has 1.5 times the mass of the other. if 7500 J were released in the explosion, how much kinetic energy did each piece acquire?

How do i solve this and what is the answer?

Initially, the object has some energy, and after the explosion, the two pieces have a total (kinetic) energy 7500 J less than what the whole object had before. Also, momentum must be conserved, so the product of the total mass and initial velocity must equal the sum of the final masses and velocities.

The variables you'll be dealing with are $v_1$ (the initial velocity of the whole object), $m_A$ (the mass of the smaller piece after explosion), $v_{2A}$ (the velocity of the smaller piece after explosion), and $v_{2B}$ (the velocity of the larger piece after explosion).