Question

You are hungry and decide to go to your favorite neighborhood fast-food restaurant. You leave your apartment and take the elevator 10 flights down (each flight is 3.0 m) and then go 15 m south to the apartment exit. You then proceed 0.2 km east, turn north, and go 0.1 km to the entrance of the restaurant.
A. Find the displacement from your apartment to the restaurant.
B. How far did you travel along the path you took from your apartment to the restaurant?
C. What is the magnitude of the displacement you calculated in part A?

Answer 1

Answer:

Explanation:

first displacement, d' = 10 x 3 = 30 m vertically downward

second displacement, d'' = 15 m due south

third displacement, d''' = 0.2 km due east  = 200 m due east

forth displacement, d'''' = 0.1 km due north = 100 m due north

Write the displacements in the vector form.

$d' = -30\widehat{k}$

$d'' = - 15 \widehat{j}$

$d''' = 200 \widehat{i}$

$d'''' = 100 \widehat{j}$

(A) The total displacement is given by

$\overrightarrow{d} =d' + d'' + d''' + d''''$

$\overrightarrow{d} = 200 \widehat{i} + 85 \widehat{j} -30\widehat{k}$

(B) The total distance traveled is

d = 30 + 15 + 200 + 100

d = 345 m

(C) The magnitude of the displacement is

$d = \sqrt{200^{2}+85^{2}+30^{2}}$

d = 239.22 m