An aeroplane flying horizontally at a height of 3 Km, above the

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11.

An aeroplane flying horizontally at a height of 3 Km, above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is

  • 230.63 m/sec

  • 230.93 m/sec

  • 235.85 m/sec

  • 235.85 m/sec


B.

230.93 m/sec


AB = CD = 3000 metre
A and C  = Positions of aeroplane
angle AOB space equals space 60 degree semicolon space space space angle COD space equals space 30 degree
In ΔOAB,
      tan space 60 degree space equals space AB over OB

rightwards double arrow space space square root of 3 space equals space 3000 over OB
rightwards double arrow space space OB space equals space fraction numerator 3000 over denominator square root of 3 end fraction space equals space 1000 square root of 3 space metre
In ΔOCD,
tan space 30 degree space equals space CD over OD
rightwards double arrow space space fraction numerator 1 over denominator square root of 3 end fraction space equals space 3000 over OD
rightwards double arrow space space OD space space equals space 3000 square root of 3 space metre
therefore space space BD space equals space left parenthesis 3000 square root of 3 space minus space 1000 square root of 3 right parenthesis space metre space equals space 2000 square root of 3 space metre
∴  Speed of aeroplane
   space equals space open parentheses fraction numerator 2000 square root of 3 over denominator 15 end fraction close parentheses straight m divided by sec.
equals space open parentheses fraction numerator 2000 space cross times space 1.732 over denominator 15 end fraction close parentheses space straight m divided by sec
space equals space 230.93 space straight m divided by sec


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12.

If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is

  • 60 left parenthesis square root of 3 plus 1 right parenthesis space metre
  • 30 left parenthesis square root of 3 minus 1 right parenthesis space metre
  • 30 left parenthesis square root of 3 plus 1 right parenthesis space metre
  • 30 left parenthesis square root of 3 plus 1 right parenthesis space metre
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13.

The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is

  • fraction numerator straight h left parenthesis cot space straight beta space minus space cot space straight alpha right parenthesis over denominator cos space left parenthesis straight alpha space plus space straight beta right parenthesis end fraction
  • straight h space left parenthesis cot space straight alpha space minus space cot space straight beta right parenthesis
  • fraction numerator straight h left parenthesis tan space straight beta space minus space tan space straight alpha right parenthesis over denominator tan space straight alpha space tan space straight beta end fraction
  • fraction numerator straight h left parenthesis tan space straight beta space minus space tan space straight alpha right parenthesis over denominator tan space straight alpha space tan space straight beta end fraction
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14.

The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar must be raised so that its angle of elevation at the same point may be 45°, is (takeing √3 = 1.732)

  • 63.4

  • 86.6

  • 126.8

  • 128.6

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15.

From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 30° and 45°. Then the distance between the objects are

  • 180 space open parentheses 3 plus square root of 3 close parentheses straight m
  • 180 space left parenthesis 3 minus square root of 3 right parenthesis straight m
  • 180 space left parenthesis square root of 3 space minus 1 right parenthesis straight m
  • 180 space left parenthesis square root of 3 space minus 1 right parenthesis straight m
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16.

A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is

  • 80 m

  • 100 m

  • 160 m

  • 160 m

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17.

The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is

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18.

The length of a shadow of a vertical tower is fraction numerator 1 over denominator square root of 3 end fraction times its height. The angle of elevation of the Sun is

  • 30°

  • 45°

  • 60°

  • 60°

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19.

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is

  • fraction numerator straight x over denominator 2 square root of 2 end fraction
  • straight x over 4
  • straight x square root of 2
  • straight x square root of 2
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20.

An aeroplane when flying at a height of 5000m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. The vertical distance between the aeroplanes at that instant is

  • 5000 left parenthesis square root of 3 minus 1 right parenthesis space straight m
  • 5000 space left parenthesis 3 minus square root of 3 right parenthesis space straight m
  • 5000 open parentheses 1 minus fraction numerator 1 over denominator square root of 3 end fraction close parentheses straight m
  • 5000 open parentheses 1 minus fraction numerator 1 over denominator square root of 3 end fraction close parentheses straight m
1418 Views

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