PLEASE HELP!! MAsteringPhysics What is the speed of each section (relative to Earth) after the explosion?

Question

A 885 kg two-stage rocket is traveling at a speed of 5.05×10³ m/s with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass. After the explosion, the two sections move along the original line of motion at a relative speed of 2.50×10³ m/s with respect to each other.
(a) What is the speed of each section (relative to Earth) after the explosion? v₁, v₂ = ?
(b) What is the direction of motion of each section (relative to Earth) after the explosion?
Answer: Both move away from Earth.
(c) How much energy was supplied by the explosion?
[Hint: Determine the change in kinetic energy resulting from the explosion.]
I have attempted this question twice and got it wrong both times. I now have three attempts left but have already lost points. I am unsure how else to approach the problem. I browsed through Yahoo Answers to find a similar question and worked it out accordingly, but my answers were still incorrect. Please help!
My attempted answers (incorrect):
Attempt 1:
(a) v₁ = 10,100 m/s, v₂ = 7,600 m/s  
Attempt 2:
(a) v₁ = 2,500 m/s, v₂ = 0.00913 m/s

Anonymous · Accepted Answer

a) Since the stages have equal mass, one stage gains half of the change in velocity and the other stage loses half of the change in velocity, or
v1 = 5050m/s + 1250m/s = 6300 m/s
v2 = 5050m/s - 1250m/s = 3800 m/s
Note that their separation velocity = 2500 m/s
b) Correct, both are still headed away from earth (v > 0)
c) initial KE = ½  885kg  (5050m/s)² = m * 1.128e10 J
final KE = ½  (885kg/2)  (6300² + 3800²)m²/s² = 1.198e10 J
supplied energy = 6.91e8 J = 691 MJ

Anonymous

PLEASE HELP!! MAsteringPhysics What is the speed of each section (relative to Earth) after the explosion?

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