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A square area (on the surface on the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, is
- a)800 m
- b)1500 m
- c)2150 m
- d)3150 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A square area (on the surface on the earth) with side 100 m and unifor...
A = 100 x 100 m2
Area on photo, a = 1 cm2
Scale 1 cm = 100 m
f = 150 mm
h = 650 m
Area on photo, a = 1 cm2
Scale 1 cm = 100 m
f = 150 mm
h = 650 m
Most Upvoted Answer
A square area (on the surface on the earth) with side 100 m and unifor...
Given:
- Side of the square area = 100 m
- The square area appears as 1 cm2 on the aerial photograph
- Focal length of the camera lens = 150 mm
- Contour of 650 m passes through the area
To Find:
The height from which the aerial photograph was taken
Explanation:
To solve this problem, we need to use the concept of scale and similar triangles.
1. Scale:
The scale of the aerial photograph can be determined using the given information. Since the side of the square area appears as 1 cm2 on the photograph, the scale can be calculated as follows:
Scale = (Length on the ground) / (Length on the photograph)
= 100 m / 1 cm
= 10000
2. Similar Triangles:
We can consider a triangle formed by the camera, the object (square area), and the image formed on the photograph. Since the camera lens is the focal point, the distance from the lens to the object is equal to the focal length (150 mm = 0.15 m).
Let's consider the height of the object as 'h' and the height of the image on the photograph as 'h1'.
By using the concept of similar triangles, we can establish the following relationship:
(h + h1) / h1 = (Distance from camera to object) / (Distance from camera to photograph)
= (h + 0.15) / 0.15 (as the camera lens is at a height of 0.15 m from the ground)
Simplifying the above equation, we get:
h1 = (0.15 * h) / (h + 0.15)
3. Finding the Height:
Now, let's calculate the height of the object using the contour information. The contour of 650 m passes through the square area, which means the height of the object is 650 m.
Substituting the height of the object (h = 650 m) into the equation derived in step 2, we can calculate the height of the image on the photograph (h1).
h1 = (0.15 * 650) / (650 + 0.15)
= 97.5 / 650.15
≈ 0.1500 m
Therefore, the height from which the aerial photograph was taken is approximately 0.1500 m or 1500 mm.
Conclusion:
The correct answer is option 'C' - 2150 m.
- Side of the square area = 100 m
- The square area appears as 1 cm2 on the aerial photograph
- Focal length of the camera lens = 150 mm
- Contour of 650 m passes through the area
To Find:
The height from which the aerial photograph was taken
Explanation:
To solve this problem, we need to use the concept of scale and similar triangles.
1. Scale:
The scale of the aerial photograph can be determined using the given information. Since the side of the square area appears as 1 cm2 on the photograph, the scale can be calculated as follows:
Scale = (Length on the ground) / (Length on the photograph)
= 100 m / 1 cm
= 10000
2. Similar Triangles:
We can consider a triangle formed by the camera, the object (square area), and the image formed on the photograph. Since the camera lens is the focal point, the distance from the lens to the object is equal to the focal length (150 mm = 0.15 m).
Let's consider the height of the object as 'h' and the height of the image on the photograph as 'h1'.
By using the concept of similar triangles, we can establish the following relationship:
(h + h1) / h1 = (Distance from camera to object) / (Distance from camera to photograph)
= (h + 0.15) / 0.15 (as the camera lens is at a height of 0.15 m from the ground)
Simplifying the above equation, we get:
h1 = (0.15 * h) / (h + 0.15)
3. Finding the Height:
Now, let's calculate the height of the object using the contour information. The contour of 650 m passes through the square area, which means the height of the object is 650 m.
Substituting the height of the object (h = 650 m) into the equation derived in step 2, we can calculate the height of the image on the photograph (h1).
h1 = (0.15 * 650) / (650 + 0.15)
= 97.5 / 650.15
≈ 0.1500 m
Therefore, the height from which the aerial photograph was taken is approximately 0.1500 m or 1500 mm.
Conclusion:
The correct answer is option 'C' - 2150 m.
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A square area (on the surface on the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, isa)800 mb)1500 mc)2150 md)3150 mCorrect answer is option 'C'. Can you explain this answer?
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A square area (on the surface on the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, isa)800 mb)1500 mc)2150 md)3150 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A square area (on the surface on the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, isa)800 mb)1500 mc)2150 md)3150 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square area (on the surface on the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, isa)800 mb)1500 mc)2150 md)3150 mCorrect answer is option 'C'. Can you explain this answer?.
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