Final answer:
Cori is approximately 40.31 km from where she started. To find the distance, we can use the concept of displacement in physics. By representing each movement as a vector and adding them together, we can determine the total displacement and find the distance from the starting point.
Step-by-step explanation:
To find the distance Cori is from where she started, we can use the concept of displacement in physics. We can consider Cori's movements as vectors. The first movement of Cori heading south for 9 kilometers can be represented as a vector with a magnitude of 9 km in the south direction. The second movement of Cori heading east for 20 kilometers can be represented as a vector with a magnitude of 20 km in the east direction. The third movement of Cori heading south for 6 kilometers can be represented as a vector with a magnitude of 6 km in the south direction. To find the total displacement, we need to sum up these vectors.
The displacement vector of the first movement is 9 km south. The displacement vector of the second movement is 20 km east. The displacement vector of the third movement is 6 km south. To add these vectors, we can use vector addition. The displacement vector of the first movement remains the same. The displacement vector of the second movement needs to be rotated 90 degrees counter-clockwise to align with the south direction. The displacement vector of the third movement remains the same.
The sum of these vectors can be found by adding the magnitudes of the vectors and using the direction indicated by the resulting vector. The displacement vector of the first movement is 9 km south. The displacement vector of the second movement is 20 km east, which, when rotated 90 degrees counter-clockwise, becomes 20 km south. The displacement vector of the third movement is 6 km south. Adding these vectors, we get a displacement vector of 35 km south and 20 km east.
To find the magnitude of the displacement vector, we can use the Pythagorean theorem. The magnitude of the displacement vector is the square root of the sum of the squares of the components. In this case, it is the square root of (35^2 + 20^2). Evaluating this expression, we find that the magnitude of the displacement vector is approximately 40.31 km. Therefore, Cori is approximately 40.31 km from where she started.