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**1. Homework Statement**

A fireworks rocket is launched vertically upward, and explodes into two equal-mass pieces at the top of its trajectory. The pieces hit the ground at t1 and t2 seconds after the explosion. What is the rocket’s launch speed? Assume no air resistance.

**2. Homework Equations**

v

_{1}= velocity of mass (t

_{1})

v

_{2}= velocity of other mass(t

_{2})

h

_{max}= max height of rocket

**3. The Attempt at a Solution**

I found the max height by kinematic equations with ma=-mg and then rearranged that height in terms of the initial velocity of the rocket. I set up the energy equation (2m)gh

_{max}= (1/2)mv

_{1}

^{2}+(1/2)mv

_{2}

^{2}. I replaced the velocity of mass 1 with gt

_{1}and of mass 2 with gt

_{2}and solved for the initial velocity. Assuming I have done the math correctly, does this approach make sense? Am I missing a concept?