Final answer:
The woman's displacement is 2555m to the south.
Step-by-step explanation:
To determine the woman's displacement, we need to consider the distance and direction of each leg of her flight. Starting with 1275m south, we assign this a negative value. The leg where she flies north for 638m cancels out part of the initial southward displacement. Finally, she flies south again for 2918m which adds to the overall displacement. Adding the distances with their respective signs, the woman's displacement is 1275m - 638m + 2918m = 2555m to the south.