Vomiting after brainstem hemorrhage is definitely a serious matter because if the vomiting is caused by a brain-related issue, it is due to increased intracranial pressure. This type of vomiting is characterized as projectile vomiting, which is one of the three major signs of increased intracranial pressure. If the brainstem hemorrhage is extensive, it may cause local stimulation leading to cerebral vascular spasm, or issues such as obstructed brain circulation resulting in increased intracranial pressure and hydrocephalus. This increase in intracranial pressure, especially if prolonged, can lead to brain herniation, which is particularly deadly if it compresses the brainstem. Therefore, this is a very urgent and serious condition that requires immediate attention. Of course, if the vomiting is solely due to other reasons such as gastric retention or improper feeding, that would be a different matter. Projectile vomiting caused by increased intracranial pressure is highly severe.