Final answer:
The appropriate medical management for the patient's inability to urinate post-hip arthroplasty with 900 ml of urine detected is catheterization to prevent complications and discomfort from urinary retention.
Step-by-step explanation:
The most appropriate management for a 75-year-old female patient who underwent total hip arthroplasty and is now unable to void with 900 ml of urine on bladder ultrasound is catheterization. The inability to urinate postoperatively could lead to urinary retention, which may cause discomfort, bladder distension, and possibly urinary tract complications. Prompt medical intervention is necessary to relieve the retention and reduce the risk of complications. The patient should be monitored post-catheterization to ensure the return of normal bladder function.