Vectors and Scalars Graph

1. determine the total distance traveled and the displacement made.
A. 5.0 km 15 degrees east of north
B. 5.0 km 20 degrees east of south
C. 5.0 km east
D. 5.0 km 30 degrees south of west
E. 5.0 km 20 degrees east of south
F. 5.0 km 40 degrees north of west
G. 5.0 km 40 degrees west of south
H. 5.0 km 15 degrees east of north
I. 5.0 km 60 degrees west of north
J. 5.0 km east

Distance =50 km.

Displacement = 0
(we obtain the five point star)

A. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 15 degrees east of north. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the northeast direction.

B. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 20 degrees east of south. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the south-east direction.

C. The total distance traveled is 5.0 km and the displacement made is 5.0 km towards the east. So, you traveled a total distance of 5.0 km, and your displacement is 5.0 km towards the east.

D. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 30 degrees south of west. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the south-west direction.

E. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 20 degrees east of south. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the south-east direction.

F. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 40 degrees north of west. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the north-west direction.

G. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 40 degrees west of south. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the south-west direction.

H. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 15 degrees east of north. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the northeast direction.

I. The total distance traveled is 5.0 km and the displacement made is 5.0 km at 60 degrees west of north. So, you traveled a total distance of 5.0 km, but your displacement is 5.0 km in the north-west direction.

J. The total distance traveled is 5.0 km and the displacement made is 5.0 km towards the east. So, you traveled a total distance of 5.0 km, and your displacement is 5.0 km towards the east.

To determine the total distance traveled and the displacement made for each given vector, we will use trigonometry to break down the vectors into their horizontal and vertical components.

1. Vector A: 5.0 km, 15 degrees east of north

To find the horizontal and vertical components, we use trigonometry. The horizontal component is given by 5.0 km × cos(15°), and the vertical component is given by 5.0 km × sin(15°).

Horizontal component = 5.0 km × cos(15°) ≈ 4.867 km
Vertical component = 5.0 km × sin(15°) ≈ 1.290 km

The total distance traveled is the sum of the horizontal and vertical components: √((4.867 km)² + (1.290 km)²) ≈ 5.04 km.

The displacement is the straight-line distance from the starting point to the endpoint: √((4.867 km)² + (1.290 km)²) ≈ 5.04 km.

So the total distance traveled and the displacement made for vector A are approximately 5.04 km.

You can repeat this process for the remaining vectors B to J to find their total distance traveled and displacement made.