Enhanced EOC Problem 971 A spaceship of mass 230106 kg is cr

Enhanced EOC: Problem 9.71

A spaceship of mass 2.30×10⁶ kg is cruising at a speed of 4.40×10⁶ m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 4.80×10⁵ kg , is blown straight backward with a speed of 2.50×10⁶ m/s . A second piece, with mass 8.30×10⁵ kg , continues forward at 1.00×10⁶ m/s .

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Solution

Skipping relativistic effects ...

initial momentum = 2.30×10^6 kg x 4.40×10^6 m/s = 10.12e12 kgm/s
the momentum of the pieces must add up to that value. Take + direction as initial direction
piece 1: –4.80×10^5kg x 2.30×10^6m/s = –11.04 e11 = –1.104e12 kgm/s
piece 2: 8.30×10^5kg x 1.00×10^6m/s = 0.830e12

mass of piece 3 = 2.3–0.48–0.83= 0.69e6
momentum = 0.69e6V
summ up mommentums

10.12e12 = –1.104e12+0.830e12+0.69e6V
0.416e6V = 10.12e12
V = 24.33e6 m/s