Final answer:
Jeff's displacement after traveling 4 km west, 13 km south, and 10 km east is about 14.3 km in a south-easterly direction, which considers his final position relative to the starting point.
Step-by-step explanation:
To calculate Jeff's displacement, we need to consider the final position relative to the starting position and ignore the path taken. Jeff first travels 4 km west, then 13 km south, followed by 10 km east.
First, let's calculate the east-west displacement: He travels 4 km west and then 10 km east, which results in a net displacement of 6 km east (since 10 - 4 = 6).
In the north-south direction, he only travels 13 km south with no displacement back north, so his net displacement in the north-south direction is 13 km south.
To find the overall displacement, we combine these two components using the Pythagorean theorem: displacement = √(6^2 + 13^2) = √(36 + 169) = √205 km = approximately 14.3 km. So, the magnitude of Jeff's displacement is about 14.3 km in a direction that can be calculated with trigonometry, specifically the tangent function.