A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point on the path, he observes that the angle of elevation of the top of the pillar is . After walking for 10 min from in the same direction, at a point , he observes that the angle of elevation of the top of the pillar is . Then, the time taken (in minutes) by him, from to reach the pillar, is
- A.6
- B.10
- C.20
- D.5
Show answer and solution
Correct option: D
Solution
Let h be the height of the pillar, d be the distance from B to the pillar.
From B: tan60° = h/d → h = d√3
From A: tan30° = h/(d+10v) where v is speed, so AB = 10v minutes of distance.
h = (d + 10v)/√3
Setting equal: d√3 = (d + 10v)/√3 → 3d = d + 10v → 2d = 10v → d = 5v.
Time from B to pillar = d/v = 5 minutes.
From B: tan60° = h/d → h = d√3
From A: tan30° = h/(d+10v) where v is speed, so AB = 10v minutes of distance.
h = (d + 10v)/√3
Setting equal: d√3 = (d + 10v)/√3 → 3d = d + 10v → 2d = 10v → d = 5v.
Time from B to pillar = d/v = 5 minutes.
[JEE Main 2016]