Flight planning for vertical aerial photography: For an area with average ground elevation of 1000 m above datum, you need photographs on a scale of 1:30,000 using a camera with focal length 30 cm. What is the required flying height above datum (not just above ground) assuming a vertical photograph and negligible terrain relief variation?

Introduction / Context:
Flight altitude for vertical aerial photography is chosen to achieve a target photo scale. This problem tests the basic camera geometry relation between focal length, flying height above ground, and map/photo scale, then converts it to height above a reference datum by adding average ground elevation.

Given Data / Assumptions:

• Photo scale S = 1:30,000.
• Focal length f = 30 cm = 0.30 m.
• Average ground elevation h_ground = 1000 m above datum.
• Vertical photograph (tilt neglected) and uniform terrain for scale computation.

Concept / Approach:
For a truly vertical photograph over approximately level ground, the photo scale S is given by S = f / H_g, where H_g is the flying height above ground. Therefore H_g = f / S. Height above datum H_datum is then H_datum = H_g + h_ground.

Step-by-Step Solution:
Compute H_g: H_g = f / S = 0.30 m / (1/30,000) = 0.30 * 30,000 = 9,000 m.Convert to height above datum: H_datum = H_g + h_ground = 9,000 + 1,000 = 10,000 m.Select the option closest to 10,000 m.

Verification / Alternative check:
A useful mnemonic: H_g (in m) ≈ f(cm) * 300 when S = 1:30,000, because 30 cm * 30,000 = 900,000 cm = 9,000 m. Adding average elevation gives the height above datum.

Why Other Options Are Wrong:
9,000 m: height above ground, not above datum.9,500 m / 8,500 m / 11,000 m: do not satisfy the scale computation with the given f and ground elevation.

Common Pitfalls:
Confusing flying height above ground with flying height above datum, and mixing centimetres with metres when using f and S. Always convert f to metres (or keep everything in centimetres consistently) and then add the ground elevation to obtain the datum-referenced height.

Final Answer:
10,000 m.