Question

You are making a map of some of your favorite locations in town. What is the total distance that you traveled while making the map? Use your diagram to determine your final displacement from your starting point. What vector will you follow to return to your starting point?

A) 800 m
B) 1200 m
C) 1000 m
D) 1400 m

Answer 1

Distance refers to the total length of the path traveled, while displacement is the vector representing the shortest straight-line distance from start to end, including both magnitude and direction. To find the displacement, vector addition should be used.

Step-by-step explanation:

To answer a student's question regarding the total distance traveled while making a map and the final displacement from the starting point, we need to understand the concepts of distance and displacement, and how to calculate them using vector addition. Distance is a scalar quantity that represents the total path length traveled, regardless of direction, while displacement is a vector quantity representing the shortest path from the starting point to the final point, including both magnitude and direction.

Citing the provided example, if someone walks 25.0 m in a direction 49.0° north of east, then 23.0 m heading 15.0° north of east, and finally 32.0 m 68.0° south of east, the total distance walked would be the sum of these three paths, which in this case is 25.0 m + 23.0 m + 32.0 m = 80.0 m. Displacement, however, would be found by calculating the resultant vector from the starting point to the ending point, not the entire path taken.

Similarly, for a person who walks 18.0 m west and then 25.0 m north, the distance is simply the sum of these two paths (18.0 m + 25.0 m = 43.0 m), but to find the displacement, we would use vector addition to find the hypotenuse of the right-angled triangle they form, resulting in a displacement magnitude less than the total distance traveled.