Question

Problem: A spaceship of mass 1.9×10⁶ kg is cruising at a speed of 6.0×10⁶ m/s when the antimatter reactor fails, blowing the ship into three pieces. The first piece, having a mass of 4.9×10⁵ kg , is blown straight backward with a speed of 2.5×10⁶ m/s . A second piece, with mass 7.5×10⁵ kg , continues forward at 1.0×10⁶ m/s. Q: What is the speed of the third piece?

Answer 1

Since explosion is only in one direction and there is no external force applied, So

Using momentum conservation:

Pi = Pf

M*V = m1*v1 + m2*v2 + m3*v3

v3 = (M*V - m1*v1 - m2*v2)/m3

M = 1.9*10^6 kg, m1 = 4.9*10^5 kg, m2 = 7.5*10^5 kg, So

m3 = M - m1 - m2 = 1.9*10^6 - 4.9*10^5 - 7.5*10^5

m3 = 6.60*10^5 kg

Now Using given values:

v3 = (1.9*10^6*6.0*10^6 - 4.9*10^5*(-2.5*10^6) - 7.5*10^5*(1.0*10^6))/(6.60*10^5)

v3 = 18.0*10^6 m/sec = speed of the third piece

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