Question

Solve the numerical problem.

A transmitting antenna at the top of a tower has a height of 32 m and that of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight mode? The given radius of Earth is 6.4 × 10⁶ m.

Answer 1

Given: h_t = 32 m, h_r = 50 m, R = 6.4 × 10⁶ m

To find: Maximum distance or range (d)

Formula: d = `sqrt(2"Rh")`

Calculation: From the formula,

d_t = `sqrt(2"Rh"_"t")`

= `sqrt(2xx6.4xx10^6xx32)`
= 20.238 × 10³ m
= 20.238 km

d_r = `sqrt(2"Rh"_"t")`

= `sqrt(2xx6.4xx10^6xx50)`
= 25.298 × 10³ m
= 25.298 km

Now, d = d_t + d_r
= 20.238 + 25.298
= 45.536 km

The maximum distance for satisfactory communication is 45.536 km.