Question

A spaceship of mass 2.30×106 kg is cruising at a speed of 5.40×106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.10×105 kg , is blown straight backward with a speed of 2.40×106 m/s . A second piece, with mass 8.30×105 kg , continues forward at 1.20×106 m/s .

Part A What is the speed of the third piece?

Answer 1

given

M = 2.30 X 10⁶ kg

m₁ = 4.6 X 10⁵ kg

and velocity is 2.40 X 10⁶ m/s

m₂ = 8.30 X 10⁵ kg

and velocity is 1.2 X 10⁶ m/s

here the mass of third piece is m₃  

m₃ = M - ( m₁ + m₂ )

= 2.30 X 10⁶ - ( 5.10 X 10⁵ - 8.30 X 10⁵ )

= 960000 kg

using the conserving of mass then,

2.30 X 10⁶ X 5.4 X 10⁶ = - ( 5.10 X 10⁵ X 2.4 X 10⁶ ) + ( 8.30 X 10⁵ X 1.2 X 10⁶ ) + ( 960000 X V₃ )

( 960000 X V₃ ) = ( 2.30 X 10⁶ X 5.4 X 10⁶ ) + ( 5.10 X 10⁵ X 2.4 X 10⁶ ) - ( 8.30 X 10⁵ X 1.2 X 10⁶ )

( 960000 X V₃ ) = ( 1.242 X 10¹³ ) + ( 1.224 X 10¹² ) - ( 9.96 X 10¹¹ )

( 960000 X V₃ ) = 1.2648 X 10¹³

V₃ = 1.2648 X 10¹³ / 960000

V₃ = 1.3175 X 10⁷ m/s

the speed of the third piece is V₃ = 1.3175 X 10⁷ m/s