Vector displacement – problems and solutions

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

1. Question: What is vector displacement? Answer: Vector displacement is a vector quantity that describes the change in position of an object. It has both magnitude and direction, pointing directly from the starting position to the final position, regardless of the path taken.

2. Question: How is vector displacement different from distance traveled? Answer: Distance traveled represents the total length of the path taken by an object, and it’s a scalar quantity. Vector displacement, on the other hand, describes the shortest straight line distance between the starting and ending points, with a specific direction, making it a vector quantity.

3. Question: If a person walks 3 km north and then 4 km east, what is the resultant displacement? Answer: By using the Pythagoras theorem for right triangles, the resultant displacement is √3²+4² which is 5 km. The direction is northeast.

4. Question: Can the magnitude of the displacement be greater than the total distance traveled? Answer: No, the magnitude of displacement can never be greater than the total distance traveled. It can be equal if the path is a straight line or less if the path taken is not straight.

5. Question: How does one represent vector displacement graphically? Answer: Vector displacement is represented graphically by an arrow. The starting point of the arrow indicates the initial position, the tip of the arrow represents the final position, and the length of the arrow corresponds to the magnitude of the displacement.

6. Question: Why is vector addition important when calculating net displacement? Answer: Vector addition is crucial because when multiple displacements are involved, they may not all be in the same direction. By adding vectors head-to-tail, we can determine the overall or net displacement of an object after several movements.

7. Question: If an object returns to its starting point after moving around, what is its displacement? Answer: If an object returns to its starting point, its displacement is zero because the initial and final positions are the same.

8. Question: Can displacement have a negative value? Answer: Displacement itself as a vector does not have a “negative” value, but its components can. For instance, if we consider north as positive, moving south would have a negative component. It’s all about the chosen reference or coordinate system.

9. Question: Why is it said that displacement is a “resultant” vector? Answer: Displacement is referred to as a “resultant” vector because it represents the combined effect of all individual movements (or displacements) made by an object. It summarizes the overall change in position.

10. Question: How is the direction of the displacement vector determined? Answer: The direction of the displacement vector is determined by the line connecting the starting position and the final position. It points directly from the start to the end.