Here is a new Maths question for 2013
A spaceship is moving with constant velocity in deep space when an onboard explosion splits the ship into two.
If the two parts of the ship, masses M and m, still continue in the same direction and the kinetic energy released by the explosion was E, what is the difference in velocity of the two parts?
And a happy new year to all!
Change the observable frame of reference to the CM of the spaceship. Then, its velocity is 0, and its KE and P are both 0. After the explosion,
E = KE1 + KE2 = 1/2(M*v1^2 + m*v2^2)
P = 0 = M*v1 + m*v2
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v1 = -m/M*v2
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Solve for v1, v2 in terms of E, and answer is |v2 - v1|