Question

A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is the range of communication for Line of Sight (LoS) mode ?
[use radius of earth = 6400 km]

• A. 45.5 km
• B. 80.2 km
• C. 144.1 km
• D. 57.28 km

Hint:

For LoS problems, ensure all units are consistent before calculation. It's usually easiest to convert everything to SI units (meters, in this case) and then convert the final answer to kilometers if required. The formula \(d = \sqrt{2Rh}\) is derived from the Pythagorean theorem applied to the tangent from the antenna top to the Earth's surface.

Answer 1

The Correct Option is D

To find the range of communication for Line of Sight (LoS) mode, we can use the following formula for the maximum distance d (in kilometers) that can be covered:

d = \sqrt{2 \times R \times h_1} + \sqrt{2 \times R \times h_2}

where:

• R is the radius of the Earth, given as 6400 km.
• h_1 is the height of the transmitting antenna, given as 50 m.
• h_2 is the height of the receiving antenna, given as 80 m.

Note: The heights should be converted from meters to kilometers for utilizing the formula properly since the radius of Earth is given in kilometers.

Let's convert the heights:

• h_1 = \frac{50}{1000} = 0.05 km
• h_2 = \frac{80}{1000} = 0.08 km

Now, substitute these values into the formula:

\begin{align*} d &= \sqrt{2 \times 6400 \times 0.05} + \sqrt{2 \times 6400 \times 0.08} \\ &= \sqrt{640} + \sqrt{1024} \\ &= 25.3 + 32.0 \\ &= 57.3 \text{ km} \\ \end{align*}

The calculated range of the Line of Sight communication is 57.3 km, which closely matches with the given option 57.28 km.

Thus, the correct answer is 57.28 km.