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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Mathematics
Chapter
Heights and Distances

JEE Main 2016 · 3 April · Mathematics · Heights and Distances

A man is walking towards a vertical pillar in a straight path, at a...

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point AA on the path, he observes that the angle of elevation of the top of the pillar is 30°{30}^{°}. After walking for 1010 minutes from AA in the same direction, at a point BB, he observes that the angle of elevation of the top of the pillar is 60°{60}^{°} . Then the time taken (in minutes) by him, from BB to reach the pillar, isA man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he

Options

  1. A2020
  2. B55
  3. C66
  4. D1010

Correct answer

B. 55

Step-by-step solution

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

ΔQPA: \dfrac{h}{x + y} = tan{30}^{°}

→3h=x+y\to \sqrt{3}h = x + y ......\left(i\right)<br/><br/><br /><br />ΔQPB: \dfrac{h}{y} = tan{60}^{°}</p><p></p><p>\to h = \sqrt{3}y......(ii)......\left(ii\right)

From equation \left(i\right) \text{andand} \left(ii\right),weget</p><p>we get</p><p>3y = x + y</p><p></p><p>\to y = \dfrac{x}{2}<br/><br/><br /><br />∵Speedisuniform<br/><br/>Therefore,distanceSpeed is uniform<br /><br />Therefore, distancexwalkedbyhiminwalked by him in10min .

and distance \dfrac{x}{2} walked by him in 5min .

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