Levelling MCQ with answer and solution

Concept

The distance to the visible horizon from height h is d = √(h/0.0673), using the combined curvature and refraction correction.

Formula

C = 0.0673 d² (C in m, d in km); d = √(h/0.0673)

Step-by-step solution

1. Heights: observer h₁ = 0.016 km = 16 m; lighthouse h₂ = 0.144 km = 144 m. 2. d₁ = √(16/0.0673) = √(237.7) = 15.42 km. 3. d₂ = √(144/0.0673) = √(2139.7) = 46.26 km. 4. Total distance D = d₁ + d₂ = 15.42 + 46.26 = 61.68 km.

Explanation

The top of the lighthouse is just seen on the horizon. So the line of sight touches the sea surface at one point between the vessel and the lighthouse. Find the horizon distance for each height and add them.

Why the other options are wrong

B, C and D: These do not match the sum of the two horizon distances (61.68 km).

Shortcut

Because √(144) = 3 × √(16), d₂ = 3 × d₁, so D = 4 × 15.42 = 61.68 km.

Common mistake

Using only the lighthouse height, or using curvature correction 0.0785 d² without refraction.