An explosion breaks an object into two pieces, one of which has 3.20 times the mass of the other. If 8000 J were released in the explosion, how much kinetic energy did each piece acquire?

Question

I started with using KE = (1/2)mv^2 and m1v1 = m2v2. Then (1/2)m1(v1)^2 + (1/2)m2(v2)^2 = 8000J. How do I find the velocities? I tried rearranging the equations to solve for one of the unknowns, but got stuck.

Momentum is conserved. The initial momentum is zero, therefore:

m1 v1 + m2 v2 = 0 ---->

m1 v1 = m2 v2 ----->

(m1 v1)^2 = (m2 v2)^2

1/2 m1 v1^2 = 1/2 m2 v2^2 * (m2/m1)

So, you have:

KE1 + KE2 = 8000 J

and:

KE1 = (m2/m1) KE2