Conservation of Momentum of a plate

[henry3369]

Homework Statement

A plate drops onto a smooth floor and shatters into three pieces of equal mass. Two of the pieces go off with equal speeds v at right angles to one another.

1. Find the speed of the third piece.

2. Find the direction of the third piece. Assume the motion of the two pieces at right angles to one another is in the positive x and y directions.

Homework Equations

v_f(m1 + m2 + m3) = m1v1+m2v2+m3v3

The Attempt at a Solution

So I solved #1 to be v₃ = vsqrt(2).

For #2, should the direction of the third piece be theta = arctan(z/x) or arctan(y/x)? I found some attempt of the solution online and they used arctan(y/x), which confuses me because wouldn't that find the resultant vector of the x and y component?

If you do arctan(y/x) you get theta = 135 degrees while arctan(z/x) gives 234.74 degrees. Which one is correct?

 

[phinds]

I don't even understand why you would need ANY equation to tell you the answer. Draw a vector diagram and it should be obvious. The SPEED will require an equation but not the direction, unless I am seriously misunderstanding something about the problem statement.