Centre of mass of this boomerang?

[gamma-guy]

Homework Statement

I have an image with the question here: http://imgur.com/TGG9VTx.jpg
The red text is the answer. I haven't been able to get it without contradicting what I've been told.

Homework Equations

I know m₁x₁ + m₂x / m₁+m₂ is centre of mass in 2d plane, but I don't know how that applies here. Also vectorR=vectorR₁x₁ +vectorR₂m₂ / m₁ + m₂ is for the 3d, but I don't know how to apply that as well. I am dumb

The Attempt at a Solution

tried using (20i + 2j + .25k) (dividing all components by 2) then multiplying by 150 (mass of block) twice then dividing by 300. didnt get the answer.

Then tried 150(20)+150(20) / 300, got 20 as answer. Wont get 10 unless I make x = 10, which I don't why I would do that.

ANY help appreciated. Thanks

 

[Tom.G]

Since a boomerang is symmetric, why not take advantage of that?
Then, where is the center of mass of a stick with uniform cross section?
That should be enough hints to find the answer.

 

[gamma-guy]

Since a boomerang is symmetric, why not take advantage of that?
Then, where is the center of mass of a stick with uniform cross section?
That should be enough hints to find the answer.

Thank you very much for the help, but I am afraid I am not quite sure i understand?

 

[haruspex]

tried using (20i + 2j + .25k) (dividing all components by 2)

That will give you the mass centre of one stick in a particular coordinate system. But that coordinate system is tailored to that stick. You should get a very different answer for the mass centre of the other stick in that same coordinate system. You are not going to get a sensible result by adding up vectors from different coordinate systems, one for each stick.
Pick a coordinate system that makes sense for both sticks.