Direction sense with two right turns: Gopal walks 2 km straight from his school, then turns right and walks 1 km, turns right again and walks 1 km to reach home. If his home lies south-east of the school, in which direction did he begin walking from the school?
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AEast
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BWest
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CSouth
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DNorth
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ENone of these
Answer
Correct Answer: East
Explanation
Introduction / Context:The problem fixes the final relative bearing of home (south-east of school) and describes a 3-segment path with two consecutive right turns. We must infer the initial heading.
Given Data / Assumptions:
- Segment 1: 2 km, unknown initial direction.
- Segment 2: 1 km after a right turn.
- Segment 3: 1 km after another right turn.
- Home is south-east of school (positive x, negative y relative to school).
Concept / Approach:Two right turns advance the heading by 180° from the initial direction, and the two 1 km legs form perpendicular components. Test candidate initial headings and check the net displacement against “south-east.”
Step-by-Step Solution:
Assume initial East: displacement = (2, 0) + (0, −1) + (−1, 0) = (1, −1) ⇒ south-east ✔.Assume initial North: (0, 2) + (1, 0) + (0, −1) = (1, 1) ⇒ north-east ✖.Assume initial West or South produce other quadrants, not south-east.Verification / Alternative check:Only the “initial East” assumption yields a final vector with x > 0 and y < 0 (SE), matching the given relationship.
Why Other Options Are Wrong:
- North/West/South beginnings land in different quadrants or axes.
Common Pitfalls:Forgetting that the second and third segments are both 1 km; asymmetry would change the quadrant test.
Final Answer:East