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A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement?
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A person moves northwards 20 m eastward 30 m finally towards west 40 m...
Distance Traveled
The total distance traveled by the person can be calculated by adding all the individual segments of the journey.
- Northward Movement: 20 m
- Eastward Movement: 30 m
- Westward Movement: 40 m
Total Distance = 20 m + 30 m + 40 m = 90 m
Displacement
Displacement is defined as the shortest straight-line distance from the initial position to the final position, along with the direction. To calculate displacement, we need to determine the final coordinates of the person based on the movements.
1. Starting Point: Consider the initial position as the origin (0, 0).
2. After Moving North (20 m): New position = (0, 20)
3. After Moving East (30 m): New position = (30, 20)
4. After Moving West (40 m): New position = (-10, 20)
Now, to find the displacement, we calculate the straight-line distance from the origin (0, 0) to the final coordinates (-10, 20).
Using the Distance Formula:
\[
\text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- \(x_1 = 0, y_1 = 0\)
- \(x_2 = -10, y_2 = 20\)
Displacement Calculation:
\[
\text{Displacement} = \sqrt{(-10 - 0)^2 + (20 - 0)^2}
\]
\[
= \sqrt{100 + 400} = \sqrt{500} \approx 22.36 \text{ m}
\]
Summary
- Total Distance Traveled: 90 m
- Displacement: Approximately 22.36 m in the northwest direction.
The total distance traveled by the person can be calculated by adding all the individual segments of the journey.
- Northward Movement: 20 m
- Eastward Movement: 30 m
- Westward Movement: 40 m
Total Distance = 20 m + 30 m + 40 m = 90 m
Displacement
Displacement is defined as the shortest straight-line distance from the initial position to the final position, along with the direction. To calculate displacement, we need to determine the final coordinates of the person based on the movements.
1. Starting Point: Consider the initial position as the origin (0, 0).
2. After Moving North (20 m): New position = (0, 20)
3. After Moving East (30 m): New position = (30, 20)
4. After Moving West (40 m): New position = (-10, 20)
Now, to find the displacement, we calculate the straight-line distance from the origin (0, 0) to the final coordinates (-10, 20).
Using the Distance Formula:
\[
\text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- \(x_1 = 0, y_1 = 0\)
- \(x_2 = -10, y_2 = 20\)
Displacement Calculation:
\[
\text{Displacement} = \sqrt{(-10 - 0)^2 + (20 - 0)^2}
\]
\[
= \sqrt{100 + 400} = \sqrt{500} \approx 22.36 \text{ m}
\]
Summary
- Total Distance Traveled: 90 m
- Displacement: Approximately 22.36 m in the northwest direction.
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A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement?
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A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement?.
A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person moves northwards 20 m eastward 30 m finally towards west 40 m what is his distance and displacement?.
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