Help needed with physics prob please?

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) 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.

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

Take east as positive x direction, north as positive y direction and upward as positive z direction.

Then west becomes negative x direction, south becomes negative y direction and downward becomes negative z direction.

Let i,j,k be unit vectors along x,y,z axes respectively.

Taking elevator 10 flights down with each flight 3.0 m means moving down by 10*3.0 m = 30 m. So displacement = -30m k

Going 15 m south means displacement = -15m j

0.2km east means 0.2km i = 200m i

0.1km north means 0.1km j = 100m j

a)Displacement from apartment to the restaurant

= -30m k - 15m j + 200m i + 100m j

= 200m i + 85m j - 30m k

b) Distance travelled = 30m + 15m + 200m + 100m = 345 m

c) Magnitude of displacement = magnitude of 200m i + 85m j - 30m k

= sqrt(200^2 + 85^2 + 30^2) m

= sqrt(40,000 + 7,225 + 900) m

= sqrt(48,125)

= 219.37 m