Final answer:
Gabriela covered a distance of 3 km, but her displacement, which is the straight-line distance from her starting point to her final position, is approximately 2.24 km toward the southeast.
Step-by-step explanation:
The question involves concepts of distance and displacement, which are both addressed in Physics.
The distance Gabriela covered can be calculated by simply adding up the lengths of each segment of her walk. Distance is a scalar quantity and does not depend on the direction. Thus, Gabriela covered:
1 km (east) + 1 km (south) + 1 km (east) = 3 km
Displacement, on the other hand, is a vector quantity, which means it has both magnitude and direction. To calculate the displacement, we can represent Gabriela's walk graphically as a vector diagram. Her displacement would be the straight line from her starting point to her final position.
Starting at the origin, she walks 1 km east, then 1 km south, and then 1 km east again. In vector terms, her displacement would have an eastward component of 2 km (1 km + 1 km) and a southward component of 1 km. The resultant displacement vector can be found using the Pythagorean theorem:
The magnitude of the displacement vector is:
√((2 km)2 + (1 km)2) = √(5 km2) = √5 km ≈ 2.24 km toward the southeast.