Question

A square area flat on the surface of the earth with a side of 100 m appears as 100 mm² on a vertical aerial photograph. The topographic map shows that a contour of 750 m passes through the area. If the focal length of the camera is 250 mm², the height from which the aerial photograph was taken is:

• A. \(\text{3250m} \)
• B. \(\text{2500m} \)
• C. \(\text{1750m} \)
• D. \(\text{1000m} \)

Hint:

To determine the flying height (H) from a vertical aerial photograph, use the formula: \( H = S \times (H - h) + h \), where \( S = \frac{f} \) \){H - h} \) \) \).

Answer 1

The Correct Option is B

Step 1: Understanding the scale formula. The scale of a vertical aerial photograph is given by: 
\(S = \frac{\text{Photo Distance} } {\text{Ground Distance} }\)

\(= \frac{f} {H - h}\)  
where: - \(f = 250 \text{ mm}\) = 0.25 \(\text{ m} \) (focal length), 
- \( H \) = Flying height (to be determined), 
- \( h = 750m \) (elevation of the ground feature), 
- The ground distance is 100 m, and the photo distance is 100 mm (0.1 m²). 

Step 2: Finding the scale. \[ S = \frac{0.1}{100} = 1:1000 \] 
Step 3: Using the scale equation. \[ S = \frac{f} {H - h}  \] \[ 1000 = \frac{0.25}{H - 750}  \] \[ H - 750 = \frac{0.25 \times 1000} {1}  = 250 \] \[ H = 250 + 750 = 2500m \] 
Step 4: Selecting the correct option. Since the computed flying height is 2500 m, the correct answer is b. 2500m.