# Vector displacement – problems and solutions

1. A person walks from point A to point B, 600 meters north; then to point C, 400 meters west; then to point D, 200 meters south; and then finish at point E, 700 meters east. What is the magnitude of the displacement?

Solution :

__Known :__

AF = AB – BF = AB – CD = 600 – 200 = 400 m

EF = DE – DF = DE – BC = 700 – 400 = 300 m

2. A person walks 10 meters west, then 12 meters south, and then 15 meters east. What is the displacement from the original point?

3. A person walks 1 meter west, then 3 meters south, and then 5 meters east. What is the displacement from the original point?

4. What is the displacement of the object according to the figure below.

5. A person walks 80 meters north, then 80 meters east and then 20 meters south. What is the displacement of the person?

6. A person walks 6 meters east, then 6 meters south and then 2 meters east. What is the displacement of the person?

7. An object moves 40 meters east, then moves in a direction 37^{o} north of east for 100 meters, then 100 meters north. What is the displacement of the object? sin 37^{o} = 0.6.

__Known :__

__Wanted :__ The magnitude of the displacement (R)

__Solution :__

Sin 37^{o} = c / d

0.6 = c / 100

c = (100)(0.6)

c = 60 meters

The resultant vector :

8. An object moves 4√3 meters west, then 4 meters north, and then moves in a direction 60^{o} east from the north for 8 meters. What is the resultant of the displacement?

__Known :__

a = a’ = 4√3 meters

b = b’ = 4 meters

c = 8 meters

d = ……

__Wanted :__ The resultant of displacement

__Solution :__

sin 30^{o} = d / c

0.5 = d / 8

d = (0.5)(8)

d = 4 meters

**The resultant of displacement :**

R = b’ + d

R = 4 meters + 4 meters

R = 8 meters