Unknown object in the sky that did not move.

My daughter and I we heading home from school and she noticed in the Southwestern sky what appeared to be two planes.  She said that one was odd as it did not appear to be moving and we could clearly see the other plane moving with contrails behind it.
I pulled over in a parking lot to observe the sky.  She pointed out that the object appeared to be facing downwards and stationary with small V shaped contrails that came together as the object came to a point.  We could still see the other plane moving to the right of the object.
It was odd sight as we continued looking at the object it then went back from a dot to what we had first seen an object facing downwards with the same small V shaped contrails behind it.  I continued home in the hopes of viewing from my home but trees we blocking that area in the sky.