Relief displacement on vertical imagery: two equal-height towers lie 3 km and 5 km from the nadir point on opposite sides. Which statement about their height displacement magnitudes is correct?

Introduction / Context:
In photogrammetry and remote sensing, relief displacement on a vertical photo causes tall objects to lean radially away from the nadir (principal point). The magnitude of this displacement depends on the object's height and its radial distance from the nadir relative to the flying height.

Given Data / Assumptions:

• Towers A and B have equal heights.
• Distances from nadir: r_A = 3 km, r_B = 5 km.
• Both lie on opposite sides of the nadir (direction does not affect magnitude).
• Flying height H is constant and large compared with object heights.

Concept / Approach:
The standard relation for radial relief displacement is d = r * h / H, where r is ground radial distance from nadir, h is object height, and H is flying height above ground. For equal h and H, the displacement scales linearly with r.

Step-by-Step Solution:
Write displacement: d_A = r_A * h / H.Write displacement: d_B = r_B * h / H.Compare using given r values: since r_B > r_A (5 km > 3 km), d_B > d_A.Therefore, tower A's height displacement is less than tower B's.

Verification / Alternative check:
If r → 0 (at nadir), displacement tends to zero, matching the formula. Increasing r increases displacement, confirming the conclusion.

Why Other Options Are Wrong:

• B < A contradicts the linear r dependence.
• Equal displacements would require equal r, which is not the case.
• 'Towards each other' confuses direction with magnitude; in vertical photos, tall objects lean away from nadir on both sides.

Common Pitfalls:

• Mixing up radial distance on the photo with ground distance; proportionality still holds via scale.
• Forgetting displacement direction is always away from the principal point.

Final Answer:
Height displacement of A will be less than that of B