Final answer:
The nurse should monitor the child closely for signs of dehydration as a priority problem.
Step-by-step explanation:
The nurse should monitor the child closely for signs of dehydration as a priority problem. Persistent vomiting can lead to dehydration, which is a serious concern. Signs of dehydration include a marked decrease in urination, a very dry mouth and throat, feeling dizzy when standing up, and signs of severe gastrointestinal distress.