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 1.8×10⁶ m/s . A second piece, with mass 8.3×10⁵ kg , continues forward at 1.3×10⁶ m/s .

Part B) What is the speed of the third piece? Assume that the initial speed of the ship is positive

v^3= ?

Answer 1

Mass of the third piece = Total initial mass - Sum of the masses of the first two pieces.

Hence, mass of the third piece = 2.3×10⁶ kg - ( 4.7×10⁵ kg + 8.3×10⁵ kg ) = 10⁶ kg.

According to the principle of linear momentum conservation,

total initial momentum = total final momentum of all the three pieces.

So, 2.3×10⁶ kg x 6.0×10⁶ m/s = 4.7×10⁵ kg x ( - 1.8×10⁶ m/s ) + 8.3×10⁵ kg x 1.3×10⁶ m/s + 10⁶ kg x v₃ m / s

or, 1.38 x 10¹³ = 2.33 x 10¹¹ + 10⁶ x v₃

or, v₃ = ( 1.38 x 10¹³ - 2.33 x 10¹¹ ) / 10⁶

or, v₃ ~ 1.36 x 10⁷ m / s, moving forward.