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Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house?
Most Upvoted Answer
Let a cyclist start from his house . He travels 50 m along north and t...
Problem Statement
A cyclist starts from his house and travels 50m north, then 10m east, and finally 10√2m in the southwest direction. What is the cyclist's displacement from his house?
Explanation
Displacement is the shortest distance between the initial and final positions of an object, and it is a vector quantity. It is different from the distance travelled, which is the total length of the path taken by the object.
Step 1: Break down the motion into components
The motion of the cyclist can be broken down into two components:
- 50m north
- 10m east, followed by 10√2m southwest
Step 2: Calculate the displacement due to each component
The displacement due to the first component is simply 50m north.
The displacement due to the second component can be calculated as follows:
- The displacement due to the 10m east component is 10m east.
- The displacement due to the 10√2m southwest component is 10√2m at an angle of 225 degrees (southwest is halfway between south and west).
Step 3: Combine the displacements
The two displacements can be combined using vector addition. The north and south components cancel out, leaving only the east and west components.
The east component is 10m, and the west component is -10√2m (since it is in the opposite direction). Therefore, the total displacement is:
Displacement = √(10^2 + (-10√2)^2) = √(100 + 200) = √300 ≈ 17.32m
Conclusion
The cyclist's displacement from his house is approximately 17.32m, at an angle of approximately 242 degrees (measured counterclockwise from east).
Community Answer
Let a cyclist start from his house . He travels 50 m along north and t...
36.8m in north east
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Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house?
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Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house?.
Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a cyclist start from his house . He travels 50 m along north and then 10m towards east and then 10√2 m in south wast direction. What is his displacement from his house?.
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