Final answer:
The patient assessment that warrants an urgent change in the nursing plan of care is a rigid abdomen and vomiting following indigestion.
Step-by-step explanation:
The patient assessment that warrants an urgent change in the nursing plan of care is option d: Rigid abdomen and vomiting following indigestion.
A rigid abdomen and vomiting following indigestion can be indicative of a complication related to the gastric ulcer, such as perforation or penetration of the ulcer. This is a serious condition that requires immediate medical attention.
The other options, including back pain, chest pain relieved with eating or drinking water, and burning epigastric pain 90 minutes after breakfast do not indicate a critical change in the nursing plan of care.