JEE Main · 2016 · 03 Apr 2016 · Offline · Heights and Distances

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A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is

3 0^{\circ}

. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is

6 0^{\circ}

. Then the time taken (in minutes) by him, from B to reach the pillar, is:

(A)10
(B)20
(C)5✓ Correct
(D)6

Answer: (C)

Solution

Let the pillar have height

h

, with

x

the distance from B to its foot and

y = A B

. From B,

tan 6 0^{\circ} = \frac{h}{x}

, so

h = 3 x

. From A,

tan 3 0^{\circ} = \frac{h}{x + y}

, so

x + y = 3 h = 3 x

, giving

y = 2 x

. At uniform speed the time is proportional to distance, and covering

y = 2 x

took 10 minutes, so covering

x

takes 5 minutes. He reaches the pillar 5 minutes after B.

JEE Main · 2016 · 03 Apr 2016 · Offline · Single correct option

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JEE Main · 2016 · 03 Apr 2016 · Offline · Heights and Distances

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