When an object is thrown into the air, different parts of the object can follow complicated paths if the object spins as it travels. However, the centerofmass of the object will always follow a parabolic trajectory through the air.
The centerofmass is the point that moves as though all the mass is concentrated there.
The centerofmass of an object, or a collection of objects, can be found using:
X_{com}  = 

That tells you the xcoordinate of the center of mass. The ycoordinate and zcoordinate can be found from equivalent expressions.
If you have mass distributed in some way over an object instead of having a number of discrete masses, it's generally necessary to integrate to find the center of mass. The integral equation looks like:
X_{com}  = 

= 

where M is the total mass of the object 