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Sudhir leaves his home to go to the library and walks 20 m towards east. He then walks 35 m towards west and a further 5 m towards north. He then turns towards east and walks 15 m. Find the straight distance in meters between his initial and final positions.
- a)2m
- b)5m
- c)10m
- d)15m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Sudhir leaves his home to go to the library and walks 20 m towards eas...
1) Sudhir went 20 m in the East.
2) Then he took a U-turn and went 35 m in the west.
3) Then he went 5 m in the North.
4) Then he went 15 m in the East.
The path followed by Sudhir is shown in the map below:
So, the distance between the starting and the final point of Sudhir is "5 m".
2) Then he took a U-turn and went 35 m in the west.
3) Then he went 5 m in the North.
4) Then he went 15 m in the East.
The path followed by Sudhir is shown in the map below:
So, the distance between the starting and the final point of Sudhir is "5 m".
Most Upvoted Answer
Sudhir leaves his home to go to the library and walks 20 m towards eas...
Understanding Sudhir's Journey
Sudhir's movements can be tracked step by step to determine the straight-line distance between his starting and ending positions.
Step-by-Step Movement Analysis
- Initial Position: Sudhir starts at his home (let's call this point O).
- 20 m East: He walks 20 m towards the east.
- New Position: Point A (20, 0)
- 35 m West: He then walks 35 m towards the west.
- New Position: Point B (20 - 35, 0) = Point B (-15, 0)
- 5 m North: Next, he walks 5 m north.
- New Position: Point C (-15, 0 + 5) = Point C (-15, 5)
- 15 m East: Finally, he turns east and walks 15 m.
- New Position: Point D (-15 + 15, 5) = Point D (0, 5)
Calculating the Straight-Line Distance
Now, we need to find the straight-line distance between his initial position (Point O) and final position (Point D).
- Coordinates:
- Initial Position (O): (0, 0)
- Final Position (D): (0, 5)
- Distance Formula: The straight-line distance can be calculated using the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Substituting the coordinates:
Distance = √[(0 - 0)² + (5 - 0)²]
Distance = √[0 + 25]
Distance = √25
Distance = 5 m
Conclusion
Thus, the straight distance between Sudhir's initial and final positions is 5 m. Therefore, the correct answer is option B.
Sudhir's movements can be tracked step by step to determine the straight-line distance between his starting and ending positions.
Step-by-Step Movement Analysis
- Initial Position: Sudhir starts at his home (let's call this point O).
- 20 m East: He walks 20 m towards the east.
- New Position: Point A (20, 0)
- 35 m West: He then walks 35 m towards the west.
- New Position: Point B (20 - 35, 0) = Point B (-15, 0)
- 5 m North: Next, he walks 5 m north.
- New Position: Point C (-15, 0 + 5) = Point C (-15, 5)
- 15 m East: Finally, he turns east and walks 15 m.
- New Position: Point D (-15 + 15, 5) = Point D (0, 5)
Calculating the Straight-Line Distance
Now, we need to find the straight-line distance between his initial position (Point O) and final position (Point D).
- Coordinates:
- Initial Position (O): (0, 0)
- Final Position (D): (0, 5)
- Distance Formula: The straight-line distance can be calculated using the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Substituting the coordinates:
Distance = √[(0 - 0)² + (5 - 0)²]
Distance = √[0 + 25]
Distance = √25
Distance = 5 m
Conclusion
Thus, the straight distance between Sudhir's initial and final positions is 5 m. Therefore, the correct answer is option B.
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Sudhir leaves his home to go to the library and walks 20 m towards east. He then walks 35 m towards west and a further 5 m towards north. He then turns towards east and walks 15 m. Find the straight distance in meters between his initial and final positions.a)2mb)5mc)10md)15mCorrect answer is option 'B'. Can you explain this answer?
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