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An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.?
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An object first move 3m towards east , then 4m towards north then 12m ...
Understanding the Movement
The object undergoes a series of movements in three-dimensional space. To find the displacement, we will analyze each movement step by step.
Movement Breakdown
- Eastward Movement:
The object moves 3 meters towards the east.
- Northward Movement:
Next, it moves 4 meters towards the north.
- Vertical Movement:
Finally, it ascends 12 meters vertically upwards.
Visualizing the Path
Imagine the movements as vectors in a 3D coordinate system, where:
- East corresponds to the x-axis,
- North corresponds to the y-axis, and
- Upward movement corresponds to the z-axis.
Calculating Displacement
To find the displacement, we can use the Pythagorean theorem in three dimensions. The displacement vector (D) can be defined by its components:
- X Component: 3 m (East)
- Y Component: 4 m (North)
- Z Component: 12 m (Up)
The magnitude of the displacement can be calculated as follows:
D = √(X² + Y² + Z²)
Substituting the values:
D = √(3² + 4² + 12²)
D = √(9 + 16 + 144)
D = √169
D = 13 meters.
Conclusion
The total displacement of the object is 13 meters in a straight line from its starting point to its final position, illustrating the shortest path through space. This value captures the overall change in position regardless of the actual path taken.
The object undergoes a series of movements in three-dimensional space. To find the displacement, we will analyze each movement step by step.
Movement Breakdown
- Eastward Movement:
The object moves 3 meters towards the east.
- Northward Movement:
Next, it moves 4 meters towards the north.
- Vertical Movement:
Finally, it ascends 12 meters vertically upwards.
Visualizing the Path
Imagine the movements as vectors in a 3D coordinate system, where:
- East corresponds to the x-axis,
- North corresponds to the y-axis, and
- Upward movement corresponds to the z-axis.
Calculating Displacement
To find the displacement, we can use the Pythagorean theorem in three dimensions. The displacement vector (D) can be defined by its components:
- X Component: 3 m (East)
- Y Component: 4 m (North)
- Z Component: 12 m (Up)
The magnitude of the displacement can be calculated as follows:
D = √(X² + Y² + Z²)
Substituting the values:
D = √(3² + 4² + 12²)
D = √(9 + 16 + 144)
D = √169
D = 13 meters.
Conclusion
The total displacement of the object is 13 meters in a straight line from its starting point to its final position, illustrating the shortest path through space. This value captures the overall change in position regardless of the actual path taken.
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An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.?
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An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.?.
An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object first move 3m towards east , then 4m towards north then 12m vertically upward. calculate the displacement of the object.?.
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