# Momentum Explosion Problem

## Homework Statement

Hello, this is my first time posting. I'd appreciate any help.
An object with total mass mtotal = 15.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 5 kg moves up and to the left at an angle of θ1 = 21° above the –x axis with a speed of v1 = 27.6 m/s. A second piece with mass m2 = 5.5 kg moves down and to the right an angle of θ2 = 26° to the right of the -y axis at a speed of v2 = 20.2 m/s.
http://smartphysics.com/images/content/mechanics/ch13/explosion3.png [Broken]

What is the x-component and y-component of the velocity of the third piece?
What is the magnitude of the velocity of the center of mass of the pieces after the collision?

## Homework Equations

P = M*V
conservation of momentum

## The Attempt at a Solution

I already found the third mass to equal 5.1kg. Then how I tried finding x and y is kind of lengthy and I don't know if it makes sense, but I'll try to explain.
I started out with: M(final)V(final) = m1v1 + m2v2 + m3v3
And then I plugged in what I had. Since it started at rest, I know the left side is equal to zero. Then I tried plugging in what I had, but it's where I started to get confused because of the angles.
0 = 5*27.6*Vector1 + 5.5*20.2*Vector2 + 5.1*V3*Vector3
5.1*V3*Vector3 = -5*27.6*Vector1 + -5.5*20.2*Vector2
Then I flipped the directions the vectors on the left side of the equation were going to make them positive and set up triangles.
For the first mass I have a triangle with a 21degree angle and solved for the other sides, I knew the hyp would just be m1*v1,
hyp = 138, opp = 49.45, adj = 128.83
And I did the same for the second mass
hyp = 111.1, opp = 99.856, adj = 48.703
Then I added the x-direction together
49.45 + -99.856 = -50.406
and y direction
-128.83 + 48.703 = -80.127
And then I set up another triangle and use Pythagorean theorem to find the hyp
which i got to be 113.51. Then to find the angle I used tan-1(80.127/50.406) and multiplied that by the 113.51 and got 1.24.

My x and y are wrong. And I know it's way too high for velocity, so I also tried divided by the mass, but it's still wrong. I was wondering if I'm anywhere close and where I went wrong. Thank you.

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