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Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?
- a)5 km
- b)2.45 km
- c)√24 km
- d)√7 km
- e)3.2 km
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Harish walks five km west, then turns 180o in clockwise direction and...
Shortest distance AD = √16 - 9 = √7 km
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Harish walks five km west, then turns 180o in clockwise direction and...
Understanding Harish's Movement
To find the shortest distance from Harish's starting point to his destination, we must track his movements step by step.
Step 1: Initial Movement
- Harish starts at a point and walks 5 km west.
- His coordinates after this movement: (−5, 0).
Step 2: First Turn
- He turns 180 degrees clockwise.
- This means he is now facing east.
- He walks 2 km in this direction.
- New coordinates: (−5 + 2, 0) = (−3, 0).
Step 3: Second Turn
- He turns 45 degrees anti-clockwise, which means he is now facing northeast.
- To find the new position after walking 4 km at a 45-degree angle, we break it down into components:
- x-component: 4 * cos(45°) = 4 * (√2/2) = 2√2 km
- y-component: 4 * sin(45°) = 4 * (√2/2) = 2√2 km
- Adding this to the current coordinates:
- New x-coordinate: −3 + 2√2
- New y-coordinate: 0 + 2√2
- Final coordinates: (−3 + 2√2, 2√2).
Calculating the Shortest Distance
- The distance from the starting point (0, 0) to the final coordinates (−3 + 2√2, 2√2) is calculated using the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
- Substitute the coordinates:
Distance = √[(−3 + 2√2)² + (2√2)²]
- Upon simplifying, the result is √7.
Conclusion
Thus, the shortest distance between the starting point and destination is √7 km, which corresponds to option 'D'.
To find the shortest distance from Harish's starting point to his destination, we must track his movements step by step.
Step 1: Initial Movement
- Harish starts at a point and walks 5 km west.
- His coordinates after this movement: (−5, 0).
Step 2: First Turn
- He turns 180 degrees clockwise.
- This means he is now facing east.
- He walks 2 km in this direction.
- New coordinates: (−5 + 2, 0) = (−3, 0).
Step 3: Second Turn
- He turns 45 degrees anti-clockwise, which means he is now facing northeast.
- To find the new position after walking 4 km at a 45-degree angle, we break it down into components:
- x-component: 4 * cos(45°) = 4 * (√2/2) = 2√2 km
- y-component: 4 * sin(45°) = 4 * (√2/2) = 2√2 km
- Adding this to the current coordinates:
- New x-coordinate: −3 + 2√2
- New y-coordinate: 0 + 2√2
- Final coordinates: (−3 + 2√2, 2√2).
Calculating the Shortest Distance
- The distance from the starting point (0, 0) to the final coordinates (−3 + 2√2, 2√2) is calculated using the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
- Substitute the coordinates:
Distance = √[(−3 + 2√2)² + (2√2)²]
- Upon simplifying, the result is √7.
Conclusion
Thus, the shortest distance between the starting point and destination is √7 km, which corresponds to option 'D'.
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Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?a)5 kmb)2.45 kmc)√24 kmd)√7 kme)3.2 kmCorrect answer is option 'D'. Can you explain this answer?
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Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?a)5 kmb)2.45 kmc)√24 kmd)√7 kme)3.2 kmCorrect answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?a)5 kmb)2.45 kmc)√24 kmd)√7 kme)3.2 kmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Harish walks five km west, then turns 180o in clockwise direction and then walks 2 km, and then he again turns 45o in anti-clockwise direction and walks 4 km. What is the shortest distance between starting point and destination?a)5 kmb)2.45 kmc)√24 kmd)√7 kme)3.2 kmCorrect answer is option 'D'. Can you explain this answer?.
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