The angle of elevation of an aeroplane from a point on the ground is 60 deg. Aft

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Question
The angle of elevation of an aeroplane from a point on the ground is 60 deg. After flying for 30 seconds, the angle of elevation changes to 30 deg. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?
Options
A. 50?3
B. 100?3
C. 200?3
D. 300?3

Correct Answer

100?3

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Height and Distance problems

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1. The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are 30� and 60� respectively. What is the height (in metres) of building?
Options
A. 42
B. 20?3
C. 24?3
D. 48

2. The angles of elevation of the top of a tree 220 meters high from two points lie on the same plane are 30� and 45�. What is the distance (in metres) between the two points?
Options
A. 193.22
B. 144.04
C. 176.12
D. 161.05

3. The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30� and the angle of depression of the image of the aeroplane in the water of the lake is 60�. The height of the aeroplane from the water-surface of the lake is
Options
A. 60 m
B. 45 m
C. 50 m
D. 75 m

4. A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60� and 30�respectively. Distance between the two ships, in metres is
Options
A. 1000?3
B. 1000/?3
C. 500?3
D. 500/?3

5. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
Options
A. 4 m
B. 7 m
C. 9 m
D. 6 m

6. A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450?3 metres from point P observes that angle of elevation of the balloon is 60 deg. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?
Options
A. 4.25
B. 3.75
C. 4.5
D. 3.45

7. On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45 to 60 deg. What will be the height (in metres) of the building?
Options
A. 50(3 + ?3)
B. 100(?3 + 1)
C. 150
D. 100?3

8. The upper part of a tree broken over by the wind make an angle of 60 deg with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?
Options
A. 84.14
B. 93.3
C. 98.25
D. 120.24

9. The height of a tower is 300 meters. When its top is seen from top of another tower,then the angle of depression is 60�. The horizontal distance between the bases of the two towers is 120 metres. What is the height (in metres) of the small tower?
Options
A. 88.24
B. 106.71
C. 92.15
D. 112.64

10. From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?
Options
A. 720
B. 960
C. 840
D. 1030

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