Rachel's Displacement:

To find the magnitude of Rachel's overall displacement, we need to calculate the net displacement by considering the distance and direction of each individual movement she made.

Step 1: Southward Movement
Rachel walked 2.0 meters south. Since she moved in a straight line, the distance covered is equal to the displacement in this case. Therefore, the displacement due to this movement is 2.0 meters south.

Step 2: Westward Movement
Rachel then made a right-hand turn and walked 16.0 meters west. Again, since she moved in a straight line, the distance covered is equal to the displacement in this case. Therefore, the displacement due to this movement is 16.0 meters west.

Step 3: Northward Movement
Rachel turned right again and walked 24.0 meters north. Similar to the previous steps, the distance covered is equal to the displacement in this case. Therefore, the displacement due to this movement is 24.0 meters north.

Step 4: Westward Movement
Finally, Rachel turned left and walked 36.0 meters west. As before, the distance covered is equal to the displacement in this case. Therefore, the displacement due to this movement is 36.0 meters west.

Calculating the Net Displacement:
To find the net displacement, we can add up the displacements in the x and y directions separately.

In the x-direction (east/west), Rachel moved 16.0 meters west and then an additional 36.0 meters west. Therefore, the net displacement in the x-direction is 16.0 + 36.0 = 52.0 meters west.

In the y-direction (north/south), Rachel moved 24.0 meters north and 2.0 meters south. Therefore, the net displacement in the y-direction is 24.0 - 2.0 = 22.0 meters north.

Calculating the Magnitude of the Overall Displacement:
The magnitude of the overall displacement is the straight-line distance between the starting point and the final position. Using the Pythagorean theorem, we can calculate the magnitude of the displacement.

Magnitude of displacement = sqrt((net displacement in x-direction)^2 + (net displacement in y-direction)^2)
= sqrt((52.0)^2 + (22.0)^2)
= sqrt(2704 + 484)
= sqrt(3188)
≈ 56.47 meters

Therefore, the magnitude of Rachel's overall displacement is approximately 56.47 meters.