Find Velocity Components of Exploding Ball

[mikefitz]

A ball, initially at rest at the coordinate origin, explodes into three equal pieces. After explosion, one piece moves along x-axis with velocity VX1 = 4.00 m/s and another piece move with velocity: VX2 = 3.83 m/s and VY2 = 9.07 m/s. What are the velocity components for the third piece?

This confuses me because I am unsure of what direction the third piece would travel after the explosion. It could go into second quadrant and have an negative x component; it could go into the third quadrant and have both negative x and y components.

How do I begin this problem?

 

[berkeman]

Hint 1 -- they said "three equal pieces", by which you can assume equal mass.

Hint 2 -- Use conservation of linear momentum in 3 dimensions. What was the net linear momentum in each of the 3 coordinates before the explosion?

 

[mikefitz]

p=mv
since v=0, then initial momentum of the three coordinates = 0.

Knowing this, what step should I take next? I can't seem to think outside the box on this one...

 

[berkeman]

p=mv
since v=0, then initial momentum of the three coordinates = 0.

Knowing this, what step should I take next? I can't seem to think outside the box on this one...

Good, and since p and v are vectors in 3-space, you can write the 3 sums for the 3 coordinate axes and set them equal to zero, right? That should give you the answers you need.

 

[mikefitz]

thanks a lot@!