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A man is walking towards a vertical pill...

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 `30^(@)`. 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 `60^(@)` . Then the time taken (in minutes) by him, from B to reach the pillar is :

A

6

B

10

C

20

D

15

Text Solution

Verified by Experts

The correct Answer is:
D
Let v metre/minute be the speed of the man and PQ by pillar of height h metres. It is given that AB=10v. `BQ=v_1`. In triangles AQP and BQP , we have
tan `30^@=h/(10v+BQ)` and tan `60^@=h/(BQ)`

`rArr sqrt3h=10v +BQ`
`rArr BQ=5v rArr vt =5u rArr t =5`
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OBJECTIVE RD SHARMA ENGLISH-HEIGHTS AND DISTANCES-Exercise
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  2. The angle of elevation of the top of the tower observed from each of t...

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  3. A flag staff of 5m high stands on a building of 25m high. At an obse...

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  4. ABC is a triangular park with AB=AC=100 m .A clock tower is situated a...

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  5. If a flag-staff of 6 m height placed on the top of a tower throws a sh...

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  6. The angle of elevation of the top of an incomplete vertical pillar at ...

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  7. The top of a hill observed from the top and bottom of a building of he...

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  8. The angles of elevation of a cliff at a point A on the ground and at a...

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  9. The angle of elevation of a cloud from a point h mt. above is theta^@ ...

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  10. On the level ground, the angle of elevation of a tower is 30^(@). O...

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  11. Each side of an equilateral triangle subtends an angle of 60^(@) at th...

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  12. The angle of elevation of the top of a tower at any point on the groun...

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  13. Form the top of a light house 60 m high with its base at the sea-level...

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  14. A person standing on the bank of a river observes that the angle subte...

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  15. AB is a vertical pole. The end A is on the level ground .C is the midd...

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  16. A tree is broken by wind, its upper part touches the ground at a point...

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  17. about to only mathematics

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  18. A tower subtends an angle alpha at a point A in the plane of its...

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  19. The angle of elevation of the top of a tower standing on a horizontal ...

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  20. From an aeroplane vertically above a straight horizontal road, the ...

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  21. A vertical tower stands on a declivity which is inclined at 15^(@) to ...

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