Vector displacement – problems and solutions

Вектордың ығысуы – мәселелер және шешімдер

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 ауыстыру?

Шешімі:

Vector displacement – problems and solutions 1

Белгілі:

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

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

Vector displacement – problems and solutions 2

2. A person walks 10 метрs west, содан кейін 12 метрs south, содан соң 15 метрs east. What is the displacement from the original point?

Vector displacement – problems and solutions 3

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

Vector displacement – problems and solutions 4 4. What is the displacement of the object according to the figure below.

Vector displacement – problems and solutions 5

Vector displacement – problems and solutions 6

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

Vector displacement – problems and solutions 7

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

Vector displacement – problems and solutions 8

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.

Сондай-ақ, қараңыз Толқындардың сипаттамалары – мәселелер және оларды шешу жолдары

Белгілі:

Vector displacement – problems and solutions 9

Қажетті: The magnitude of the displacement (R)

Шешімі:

Күнә 37^o = c / d

0.6 = c / 100

c = (100)(0.6)

c = 60 meters

Vector displacement – problems and solutions 10

The resultant vector :

Vector displacement – problems and solutions 11

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?

Vector displacement – problems and solutions 12 Белгілі:

a = a’ = 4√3 meters

b = b’ = 4 meters

c = 8 meters

d = ……

Қажетті: The resultant of displacement

Шешімі:

күнә 30^o = d / c

0.5 = d / 8

d = (0.5)(8)

d = 4 метр

Vector displacement – problems and solutions 13

The resultant of displacement :

R = b’ + d

R = 4 meters + 4 meters

R = 8 meters

1. Сұрақ: What is vector displacement? Жауап: 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. Сұрақ: How is vector displacement different from distance traveled? Жауап: 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.

Сондай-ақ, қараңыз Жасырын жылу Балқу жылуы Булану жылуы – мәселелер мен шешімдер

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

4. Сұрақ: Can the magnitude of the displacement be greater than the total distance traveled? Жауап: 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. Сұрақ: How does one represent vector displacement graphically? Жауап: 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. Сұрақ: Why is vector addition important when calculating net displacement? Жауап: 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.

Сондай-ақ, қараңыз Тұрақты үдеумен қозғалыс – мәселелер және шешімдер

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

8. Сұрақ: Can displacement have a negative value? Жауап: 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. Сұрақ: Why is it said that displacement is a “resultant” vector? Жауап: 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. Сұрақ: How is the direction of the displacement vector determined? Жауап: 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.