Solving 3D Momentum Problem: Find Piece Velocity & Direction

[antiflag403]

I am having quite a bit of trouble with this problem. I would greatly appreciate any and all help and advice. Here's the problem:

A fire cracker is thrown with velocity 12.0 m/s [W]. While moving in this direction, it explodes into two pieces. One piece has a mass of 2.1 g and moves with velocity 10.0 m/s [W 70 S] What is the velocity of the other piece which has a mass of 1.1 g?

Ok. So far I understand that the fire cracker's momentum is
Pfc=12m/s(3.3 g)= 39.6 gm/s
The first pieces momentum is
P1= 2.1 g(10m/s)= 21 gm/s

i am having trouble deciding how to approach finding the velocity of the other peice.

Do i use P total (before)= P total (after)?
And once I find the velocity how do i figure out which direction the piece is moving?

Thanks for any help you smart people can provide.

 

[Tide]

Exactly - total momentum is conserved. Just remember that momentum is a vector so each component of momentum will be conserved as well.

 

[antiflag403]

Thanks for the reply tide, it helped a lot.
Once i have figured the velocity of this second piece, how do i go about finding which direction the piece is moving in. Will it be opposite to the other piece? or is there some type of trig that can be used?
Thanks again

 

[Doc Al]

Once i have figured the velocity of this second piece, how do i go about finding which direction the piece is moving in. Will it be opposite to the other piece? or is there some type of trig that can be used?

The velocity will have components in the x and y directions. Draw them and use some trig to find the angle.

As Tide explained, momentum is a vector. Each component is separately conserved. So start off by assigning a coordinate system: for example, let East be the +x direction, North be the +y direction. Now find:
(1) The components of the total (original) momentum
(2) The components of the momentum of the first piece

Then, using conservation of momentum, you can figure out:
(3) The components of the momentum of the second piece, and thus its velocity