Suppose that an object starts at point a and travels in an arc to point b. the trajectory of the object is defined by what two measurements?

The trajectory path is the path that a moving object follows through space as a function of time. Mathematically, a trajectory can be defined by the geometry of the path through which it traveled or by by the position of the object over time. 
The geometry definition involves the vertical and the horizontal distances of the object from the ground.

Nation of conflicting ethnic groups