Question

A spaceship of mass 2.3×10⁶ kg is cruising at a speed of 6.0×10⁶ m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 4.7×10⁵ kg , is blown straight backward with a speed of 2.2×10⁶ m/s . A second piece, with mass 7.9×10⁵ kg , continues forward at 1.3×10⁶ m/s .

Answer 1

mass of space ship M = 2.3E+6 kg

initial speed = 6.0E+6 m/s

Total momentum p = 2.3E+6 * 6.0E+6 = 13.8E+12 kg-m/s

after break:

mass of first piece m₁ = 4.7E+5 kg

speed v₁ = -2.2E+6 m/s

momentum p₁ = -10.34 E+11 kg-m/s

mass of 2nd piece m₂ = 7.9E+5 kg

speed v₂ = 1.3E+6 m/s

momentum p₂ = 7.9E+5*1.3E+6 = 10.27E+11 kg-m/s

mass of the third piece m₃ = 2.3E+6 - ( 4.7E+5 + 7.9E+5) = 10.4E+5 kg

Total momentum is conserved during the breakup

momentum of the third piece p₃ = p - (p₁+p₂) = 13.8E+12 - (-10.34E+11 + 10.27E+11)

= 13.87 E+12 kg-m/s

speed of the third piece v₃ = p₃/m₃ = 13.87E+12/10.4E+5 = 13.34E+6 m/s

third piece continues straight forward.