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Ganesh cycles towards South-West a distance of 8m, then he moves towards East a distance of 20m. Then, he moves towards North-East, a distance of 8m, then he moves towards West, a distance of 6m. From there, he moves towards North-East, a distance of 2m. Then he moves towards West, a distance of 4 m and then towards South-West 2m and stops at that point. How far is he from the starting point?
- a)12m
- b)10m
- c)8m
- d)6m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Ganesh cycles towards South-West a distance of 8m, then he moves towa...
From diagram distance from starting point
= 20 - 6 + 4
= 20 - 10 = 10m
Most Upvoted Answer
Ganesh cycles towards South-West a distance of 8m, then he moves towa...
To find out how far Ganesh is from the starting point, we need to determine the net displacement from the starting point. We can break down Ganesh's movements into different components and calculate the net displacement in each direction.
1. South-West: Ganesh moves 8m towards the South-West direction. This can be broken down into components of 8m towards the South and 8m towards the West.
2. East: Ganesh moves 20m towards the East direction. This adds 20m towards the East.
3. North-East: Ganesh moves 8m towards the North-East direction. This can be broken down into components of 8m towards the North and 8m towards the East.
4. West: Ganesh moves 6m towards the West direction. This subtracts 6m towards the West.
5. North-East: Ganesh moves 2m towards the North-East direction. This can be broken down into components of 2m towards the North and 2m towards the East.
6. West: Ganesh moves 4m towards the West direction. This subtracts 4m towards the West.
7. South-West: Ganesh moves 2m towards the South-West direction. This can be broken down into components of 2m towards the South and 2m towards the West.
Calculating the net displacement in each direction:
- North: 8m + 2m = 10m (North direction is positive)
- South: 8m + 2m = 10m (South direction is negative)
- East: 20m + 8m + 2m = 30m (East direction is positive)
- West: 8m + 6m + 4m + 2m = 20m (West direction is negative)
Now we can calculate the net displacement using the Pythagorean theorem:
Net displacement = √(North^2 + South^2 + East^2 + West^2)
= √(10^2 + (-10)^2 + 30^2 + (-20)^2)
= √(100 + 100 + 900 + 400)
= √(1500)
= 38.73m
Therefore, Ganesh is approximately 38.73m from the starting point. Since none of the given options match the calculated answer, it seems there may be an error in the question or the answer choices.
1. South-West: Ganesh moves 8m towards the South-West direction. This can be broken down into components of 8m towards the South and 8m towards the West.
2. East: Ganesh moves 20m towards the East direction. This adds 20m towards the East.
3. North-East: Ganesh moves 8m towards the North-East direction. This can be broken down into components of 8m towards the North and 8m towards the East.
4. West: Ganesh moves 6m towards the West direction. This subtracts 6m towards the West.
5. North-East: Ganesh moves 2m towards the North-East direction. This can be broken down into components of 2m towards the North and 2m towards the East.
6. West: Ganesh moves 4m towards the West direction. This subtracts 4m towards the West.
7. South-West: Ganesh moves 2m towards the South-West direction. This can be broken down into components of 2m towards the South and 2m towards the West.
Calculating the net displacement in each direction:
- North: 8m + 2m = 10m (North direction is positive)
- South: 8m + 2m = 10m (South direction is negative)
- East: 20m + 8m + 2m = 30m (East direction is positive)
- West: 8m + 6m + 4m + 2m = 20m (West direction is negative)
Now we can calculate the net displacement using the Pythagorean theorem:
Net displacement = √(North^2 + South^2 + East^2 + West^2)
= √(10^2 + (-10)^2 + 30^2 + (-20)^2)
= √(100 + 100 + 900 + 400)
= √(1500)
= 38.73m
Therefore, Ganesh is approximately 38.73m from the starting point. Since none of the given options match the calculated answer, it seems there may be an error in the question or the answer choices.
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Ganesh cycles towards South-West a distance of 8m, then he moves towards East a distance of 20m. Then, he moves towards North-East, a distance of 8m, then he moves towards West, a distance of 6m. From there, he moves towards North-East, a distance of 2m. Then he moves towards West, a distance of 4 m and then towards South-West 2m and stops at that point. How far is he from the starting point?a)12mb)10mc)8md)6mCorrect answer is option 'B'. Can you explain this answer?
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