וועקטאָר דיספּלייסמאַנט – פּראָבלעמען און לייזונגען
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?
לייזונג:
באַקאַנט:
AF = AB – BF = AB – CD = 600 – 200 = 400 m
EF = DE – DF = DE – BC = 700 – 400 = 300 m
2. A person walks קסנומקס מעטערswest, דעמאָלט קסנומקס מעטערs south, און דעמאָלט קסנומקס מעטערs 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 = קסנומקס.
באַקאַנט:
געוואָלט: The magnitude of the displacement (R)
לייזונג:
אָן 37o = c / d
0.6 = c / 100
c = (100)(0.6)
c = 60 meters
דער רעזולטירנדיקער וועקטאָר:
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?
באַקאַנט:
a = a’ = 4√3 meters
b = b’ = 4 meters
c = 8 meters
d = ……
געוואָלט: The resultant of displacement
לייזונג:
זינד 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
1. פראגע: What is vector displacement? ענטפער: 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. פראגע: How is vector displacement different from distance traveled? ענטפער: 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. פראגע: If a person walks 3 km north and then 4 km east, what is the resultant displacement? ענטפער: By using the Pythagoras theorem for right triangles, the resultant displacement is √32+42 which is 5 km. The direction is northeast.
4. פראגע: Can the magnitude of the displacement be greater than the total distance traveled? ענטפער: 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. פראגע: How does one represent vector displacement graphically? ענטפער: 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. פראגע: Why is vector addition important when calculating net displacement? ענטפער: 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. פראגע: If an object returns to its starting point after moving around, what is its displacement? ענטפער: If an object returns to its starting point, its displacement is zero because the initial and final positions are the same.
8. פראגע: Can displacement have a negative value? ענטפער: 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. פראגע: Why is it said that displacement is a “resultant” vector? ענטפער: 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. פראגע: How is the direction of the displacement vector determined? ענטפער: 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.
