Fireworks Problem: Find Speed & Distance of Fragments

[iwonde]

Homework Statement

A fireworks rocket is fired vertically upward At its maximum height of 80.0 m, it explodes and breaks into two pieces, one with mass 1.40 kg and the other with mass 0.28 kg. In the explosion, 860 J of chemical energy is converted to kinetic energy of the two fragments.
(a) What is the speed of each fragment just after the explosion?
(b) It is observed that the two fragments hit the ground at the same time. what is the distance between the points on the ground where they land? Assume that the ground is level and air resistance can be ignored.

Homework Equations

Center of Mass:
MV_cm = P

The Attempt at a Solution

I don't know how to approach this problem.

 

[JaWiB]

What the firework's velocity at its maximum height? Its momentum?

After it explodes, what is the sum of the two objects momenta?

If you can answer those questions, you should be able to write an equation including both unknown velocities. Then see if you can find a second equation given the information in the problem.

 

[iwonde]

The velocity at the maximum height is zero, so it's momentum at that point is zero.

After it explodes: (m_1)(v_1)+(m_2)(v_2) = 0
From the problem, (1/2)(m_1 + m_2) v^2 = 860 J
I'm trying to solve for v_1 and v_2.

Is my second equation correct?

 

[JaWiB]

The 860J goes into both fragments, so you have two velocities in the second equation, not one.