Question

Why do we vomit?
Which part of the brain controls this??

Answer 1

The area postrema is a medullary structure in the brain that controls vomiting. We vomit either of disgust, disease or because your sick. 

Answer 2

Vomit is an reflex of the body to irradicate the irritant in the stomach food particles. This is controlled by medulla region of hind brain where the vomit center are located.
I hope have solved you queries