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 37o north of east for 100 meters, then 100 meters north. What is the displacement of the object? sin 37o = 0.6.
Known :
Wanted : The magnitude of the displacement (R)
Solution :
Sin 37o = 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 60o 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 30o = 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
