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A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?
Most Upvoted Answer
A student moves √2x km east from his residence and then moves x km nor...
- Analysis
Given the student's movements, we need to determine the shortest distance between his residence and the school. To find the shortest distance, we can use the concept of vector addition to determine the net displacement of the student.
- Calculations
1. The student moves √2x km east and x km north, which can be represented as a vector (√2x)i + xj.
2. Then, the student moves x km north-east, which can be represented as a vector (x/√2)i + (x/√2)j.
3. Next, the student takes a turn of 90° to the right and moves x km, which can be represented as a vector xj.
4. To find the net displacement, we add all the vectors together:
Net displacement = (√2x + x/√2)i + (x + x/√2 + x)j
= ((√2 + 1/√2)x)i + ((1 + 1/√2)x)j
- Shortest Distance
The shortest distance between the student's residence and the school is the magnitude of the net displacement vector.
Using the distance formula:
Shortest distance = √[((√2 + 1/√2)x)² + ((1 + 1/√2)x)²]
= √[(2 + 2√2 + 1/2)x² + (1 + 2 + 1/2)x²]
= √[(5 + 2√2)x² + (3)x²]
= √[8x² + 3x²]
= √11x²
= √11x
Hence, the shortest distance of the school from his residence is √11x km.
Given the student's movements, we need to determine the shortest distance between his residence and the school. To find the shortest distance, we can use the concept of vector addition to determine the net displacement of the student.
- Calculations
1. The student moves √2x km east and x km north, which can be represented as a vector (√2x)i + xj.
2. Then, the student moves x km north-east, which can be represented as a vector (x/√2)i + (x/√2)j.
3. Next, the student takes a turn of 90° to the right and moves x km, which can be represented as a vector xj.
4. To find the net displacement, we add all the vectors together:
Net displacement = (√2x + x/√2)i + (x + x/√2 + x)j
= ((√2 + 1/√2)x)i + ((1 + 1/√2)x)j
- Shortest Distance
The shortest distance between the student's residence and the school is the magnitude of the net displacement vector.
Using the distance formula:
Shortest distance = √[((√2 + 1/√2)x)² + ((1 + 1/√2)x)²]
= √[(2 + 2√2 + 1/2)x² + (1 + 2 + 1/2)x²]
= √[(5 + 2√2)x² + (3)x²]
= √[8x² + 3x²]
= √11x²
= √11x
Hence, the shortest distance of the school from his residence is √11x km.
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A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?
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A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?.
A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student moves √2x km east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of 90∘ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?.
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