Conservation of momentum of plate drop

[romy]

Hi, i was wondering if anybody can help me with the following problem:

A plate drops onto a smooth floor and shatters into 3 pieces of equal mass. 2 of the pieces go off with equal speeds v at right angles to one another. How do I find the speed and direction of the third piece?

I know that the net momentum is conserved if the net external force acting on the system is zero, how can I apply this, any suggestions to which equations I can use?

 

[e(ho0n3]

I know that the net momentum is conserved if the net external force acting on the system is zero, how can I apply this, any suggestions to which equations I can use?

If momentum is conserved, then the change in momentum is 0 (i.e. $\Delta p = 0$). What is the problem?

 

[HallsofIvy]

Since two pieces go at right angles to one another, set up a coordinates system using those directions as x and y axes: The velocity vectors are (v, 0) and (0, v) and so the momentum vectors are (mv,0) and (0,mv). The total momentum of those two pieces is (mv, mv).

The total momentum of all three pieces must be 0 since the only forces involved are vertical. What is the momentum vector of the third piece?