TIGO 3G 1005 PM sessionmasteringphysicscom C Problem 965 Mas

TIGO 3G 10:05 PM session.masteringphysics.com C Problem 9.65 MasteringPhysics 3 of 5 Problem 9.65 A spaceship of mass 2.0x 106 kg is cruising at a speed of 4.9x106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.2x10 kg , is blown straight backward with a speed of 2.0×106 m/s A second piece, with mass 7.8× 105 kg , continues forward at 8.0× 105 m/s Part A What is the speed of the third piece? Express your answer using two significant figures. m/s q w e r ty u op

Solution

As the spaceship has no external force acting on it, we will use the principle of conservation of linear momentum to solve for the unknowns here.

So, we can write: MV = m₁v₁ + m₂v₂ + m₃v₃

Putting in the values we get:

2 x 10⁶ x 4.9 x 10⁶ = -5.2 x 10⁵ x 2 x 10⁶ + 7.8 x 10⁵ x 8 x 10⁵ + M₃V₃

or, 980 x 10¹⁰ = 62.4 x 10¹⁰ - 104 x 10¹⁰ + M₃V₃

or, 1021.6 x 10¹⁰ = M₃V₃

Also, M3 = 20 x 10^5 - 13 x 10^5 = 7 x 10^5

That is, V₃ = 145.943 x 10 ⁵ m/s

The positive sign of the velocity indicates that the third mass travels forward.