Final answer:
Vanessa's heart racing and reaction to the banging on the door is controlled by her sympathetic nervous system, which induces the fight-or-flight response in emergencies.
Step-by-step explanation:
The response Vanessa is experiencing due to the sudden banging on her front door and screaming is controlled by the sympathetic nervous system. This part of the autonomic nervous system is responsible for triggering the fight-or-flight response during perceived threats. It rapidly prepares the body to respond to the emergency by accelerating the heart rate, among other physiological changes, to enhance Vanessa's ability to either fight the danger or flee from it.
By contrast, the parasympathetic nervous system would have the opposite effect, promoting relaxation and the conservation of energy once the threat has passed. The central nervous system, comprised of the brain and spinal cord, oversees the general processing of sensory information and voluntary movement, and is not directly responsible for the immediate reaction to the threat that Vanessa felt.