What is a common respiratory pattern associated with hemothorax?

Tachypnea and a productive cough are indeed common signs associated with a hemothorax. In the case of a hemothorax, which is the accumulation of blood in the pleural space, the body responds to the presence of fluid and potential lung compression by increasing the respiratory rate. This rapid breathing, or tachypnea, occurs as the body's attempt to optimize oxygenation despite the impaired lung function due to the blood accumulation.

A productive cough may also accompany a hemothorax, particularly if there is concurrent pulmonary injury or infection, which can lead to the expectoration of bloody sputum. In these instances, the lungs may be compromised, and the cough reflex may be triggered in an effort to clear the airway and help facilitate breathing.

The presence of these symptoms indicates a distress in the respiratory system and a compensatory response to the underlying pathology, making this option the most appropriate choice in describing the respiratory pattern associated with hemothorax.