Question

1. alan starts from his home and walks 1.3 km east to the library. he walks an additional 0.68 km east to a music store. from there, he walks 1.1 km north to a friends house and an additional 0.42 km north to a grocery store before he finally returns home along the same path. what is his final displacement and total distance traveled? a. displacement is 0 km and distance is 7 km. b. displacement is 0 km and distance is 3.5 km. c. displacement is 7 km towards west and distance is 7 km. d. displacement is 3.5 km towards east and distance is 3.5 km.

Explanation:

Step1: Define displacement and distance

Displacement is the straight - line distance from the starting point to the ending point. Distance is the total length of the path traveled.

Step2: Analyze displacement

Since Alan returns to his home (the starting point), the straight - line distance between the starting and ending points is 0 km.

Step3: Calculate the one - way distance

The east - ward distance is $1.3 + 0.68=1.98$ km. The north - ward distance is $1.1 + 0.42 = 1.52$ km. The one - way distance is $1.98+1.52 = 3.5$ km.

Step4: Calculate the total distance

He travels the one - way path and then returns along the same path. So the total distance is $2\times3.5=7$ km.

Answer:

A. Displacement is 0 km and distance is 7 km.