GATE CE 2018 Set 1 — Question 4
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Tower A is m tall and tower B is m tall. They are m apart. A horizontal skywalk connects the floors at m in both the towers. If a taut rope connects the top of tower A to the bottom of tower B, at what distance (in meters) from tower A will the rope intersect the skywalk?
- A.22.22
- B.50
- C.57.87
- D.77.78
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Correct answer
(MARKS TO ALL)
Solution
Let the base of Tower A be at the origin and the base of tower B be at on a 2D plane.
The rope is a straight line connecting and . Its equation is given by:
Since represents the horizontal distance from Tower A (which is at ), the rope intersects the skywalk at a distance of m from Tower A.Note: Although the mathematical derivation leads to option (A), the official GATE 2018 answer key marked this question as 'Marks to All' (MTA).
1.Coordinates of key points:
- Top of Tower A:
- Bottom of tower B:
- The skywalk is a horizontal line at height m, extending between the towers.
The rope is a straight line connecting and . Its equation is given by:
3.Intersection with the skywalk:
To find where the rope intersects the skywalk, set :Since represents the horizontal distance from Tower A (which is at ), the rope intersects the skywalk at a distance of m from Tower A.Note: Although the mathematical derivation leads to option (A), the official GATE 2018 answer key marked this question as 'Marks to All' (MTA).
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