What is the speed of a piece of a spaceship that blew up?

[oneamp]

Homework Statement

A spaceship of mass 2.30×106kg is cruising at a speed of 5.50×106m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.20×105kg , is blown straight backward with a speed of 2.30×106m/s . A second piece, with mass 8.40×105kg , continues forward at 1.30×106m/s .

Homework Equations

The Attempt at a Solution

Using mv=p, I calculated p of each piece like this:
p1 = 1.196*10^12
p2 = 1.092*10^12
p_total = 1.265*10^13

Then I found p3 by subtracting p2+p1 from p_total.

I divided p3 by the mass of the mystery piece: p/940,000 = 1.0302*10^13

But... the answer was wrong. I also tried subtracting: p1-p2 =pt and working from there. What am I doing wrong?

Thanks

 

[nasu]

Momentum is a vector. You need to add the three momenta (after explosion) as vectors. Here, in 1D, be careful with the signs. A diagram may help.

 

[oneamp]

But it's not 1D, right? Because one goes forward, one goes back, and the mystery piece I am solving for goes off in an unspecified direction...

 

[oneamp]

I got it, thanks for that tip.

 

[Rawrr!]

I believe you are right in using the conservation of momentum to tackle this problem. The initial momentum should equal the final momentum of the combined three pieces, such that

p_initial = p₁ + p₂ + p₃

m_(total)v = m₁v₁ + m₂v₂ + m₃v₃

p_(total) = (2.3x10⁶kg)(5.50 x 10⁶m/s) = (1.265x10¹³)

p₁ = (5.20×10⁵kg)(-2.30×10⁶m/s) = (-1.20x10¹²)

p₂ = (8.40×10⁵kg)(1.30×10⁶m/s) = (1.092x10¹²)

p₃ = (9.4x10⁵kg) v₃

Because the first piece was blown backwards, it becomes important to apply the negative to its velocity component, and should look like,

(1.265x10¹³) = (-1.20x10¹²) + (1.092x10¹²) + (9.4x10⁵kg)(v₃)

It becomes simple to solve for v₃ . I assume the sign was causing your problem in the calculations. The mass of the third piece was found by the missing mass, m_(total) = m₁ + m₂ + m₃

Because the problem doesn't specify, i took the assumption that the collision only occurs in a single direction, along the x-axis, and that the velocity of each piece doesn't have to be broken down into individual x- and y-components.