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.

Part A

Determine the displacement from your apartment to the restaurant. Use unit vector notation for your answer, being sure to make clear your choice of coordinates.

Take the beginning of the journey as the origin, with north being the y-direction, east the x-direction, and the z-axis vertical.

Part B

How far did you travel along the path you took from your apartment to the restaurant?

Part C

What is the magnitude of the displacement you calculated in part

Answer 1

A) R = (200 i ^ + 100 j ^ + 30k ^) m , B) L = 223.61 m , C) R = 225.61 m

Step-by-step explanation:

Part A

This is a vector summing exercise, let's take a Reference System where the z axis corresponds to the height (flights), the x axis is the East - West and the y axis corresponds to the North - South.

Let's write the displacements

Descending from the apartment

10 flights of 3 m each, the total descent is 30 m

Z = 30 k ^ m

Offset at street level

L1 = 0.2 i ^ km

L2 = 0.1 j ^ km

Let's reduce everything to the SI system

L1 = 0.2 * 1000 = 200 i ^ m

L2 = 100 j ^ m

The distance traveled is

R = (200 i ^ + 100 j ^ + 30k ^) m

Part B

The horizontal distance traveled can be found with the Pythagorean theorem for the coordinates in the plane

L² = x² + y²

L = √ (200² + 100²)

L = 223.61 m

Part C

The magnitude of travel, let's use the Pythagorean theorem for the sum

R² = x² + y² + z²

R = √ (30² + 200² + 100²)

R = 225.61 m