Explosion mass and magnitude physics

[sam_amy]

An object with total mass mtotal = 16.5 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.7 kg moves up and to the left at an angle of θ1 = 19° above the –x axis with a speed of v1 = 26.5 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of θ2 = 24° to the right of the -y axis at a speed of v2 = 21.2 m/s.

What is the magnitude of the final momentum of the system (all three pieces)?
What is the mass of the third piece?
What is the x-component of the velocity of the third piece?

So I don't even know where to begin with this...
In class we went over Kinetic Energy of a system but not for momentum...Would it just be the sum of the masses times the sum of the velocities...? I don't know m3 or v3 though :(

 

[jackarms]

That would be the expression for momentum, but the idea here is to use the conservation of momentum. An explosion always means some internal process, so something that is not external to the system. If you look at the momentum of the object before the explosion, then it must be equal to the momentum after the explosion since there are no net external forces acting on the object, only the internal ones due to the explosion.

 

[BvU]

So I don't even know where to begin with this...

Well, you could start with the second question. Shouldn't be too hard to calculate the mass of the third piece

Then:

momentum...Would it just be the sum of the masses times the sum of the velocities...?

No. momentum is per "piece. It is the vector that has to do with amount of motion, hence mass times velocity vector": $\vec p=m\vec v$

 

[sam_amy]

Ok yes, I've figured out how to do the first two, but how do I figure out the components?

 

[BvU]

The center of mass is sitting still before the explosion. The three fragments fly off all over the place, but the center of mass still sits still, because of action = - reaction. That means the three momentum vectors add up to a vector of zero length. You have two of the three.