Question

An observer standing on a signal post between two forts situated in a straight line sees the top of both the forts. If the signal post acts as point of horizon, what is the distance between two forts, if fort A and B are 3 km and 5 km above the sea level respectively?

1. 280 km
2. 380 km
3. 580 km
4. 480 km

Answer 1

Correct Answer - Option 4 : 480 km

Concept:

Distance of visible horizon is given as,

h = 0.06735 D²

Where,

h = Height of station above datum level in meters and D = Distance of visible horizon in kilometers

Calculation:

Given,

h₁ = 3 km = 3000 m, h₂ = 5 km = 5000 m.

∵ We know that, h = 0.06735 D2

∴ \(h_1 = \text{0.06735}\times D_1^2\)

⇒ \(D_1 = \sqrt{\frac{3000}{0.06735}}\)

∴  D₁ = 211.05 km

Similarly, \(D_2 = \sqrt{\frac{5000}{0.06735}}\)

∴ D₂ = 272.47 km

∴ Distance between two forts = D₁ + D₂ 

⇒ Distance between two forts = 483.52 km