Photogrammetry (relief displacement): a minar 72 m high shows 7.2 mm of relief displacement on the photograph, and its top lies 10 cm from the principal point. Estimate the flying height of the camera.

Introduction / Context:
Relief displacement is the apparent radial shift of an elevated point on a vertical aerial photograph. It depends on the object height, its radial distance from the principal point, and the flying height above the datum. This relationship is frequently used to estimate flying height or to determine object elevation.

Given Data / Assumptions:

• Object height h = 72 m.
• Measured relief displacement d (on photo) = 7.2 mm = 0.0072 m.
• Radial distance of the top from principal point r = 10 cm = 0.10 m (on photo).
• Vertical photograph; small tilt and lens distortion neglected.

Concept / Approach:
The first-order relation for vertical photography is: d = (r * h) / H, where H is the flying height above the same datum used for h. Rearranging gives H = (r * h) / d.

Step-by-Step Solution:
Write the formula: d = (r * h) / H.Rearrange: H = (r * h) / d.Insert values: H = (0.10 * 72) / 0.0072.Compute numerator: 0.10 * 72 = 7.2.Compute division: 7.2 / 0.0072 = 1000.Thus, H ≈ 1000 m.

Verification / Alternative check:
Proportionality check: doubling r or h would double d for a fixed H; the numbers scale consistently. Units also cancel properly, yielding metres.

Why Other Options Are Wrong:
500 m and 800 m underestimate the height (they would produce larger d); 1500 m and 2000 m are too large for the observed displacement at r = 10 cm and h = 72 m.

Common Pitfalls:
Mixing ground units with photo units or using object ground distance instead of photo radial distance r; forgetting to keep d and r in the same (photo) length units.

Final Answer:
1000 m