Question

Height of the receiving and transmitting antenna in communication of a signal are 245 m and 180 m respectively. Find the maximum distance between the two antennas for proper communication.

• A. 104 km
• B. 208 km
• C. 52 km
• D. 96 km

Answer 1

The Correct Option is A

To find the maximum distance between two antennas for proper communication, we use the formula for the line-of-sight distance between two antennas. The formula is given by:

\(d = \sqrt{2 \cdot h_1 \cdot R} + \sqrt{2 \cdot h_2 \cdot R}\)

where:

• \(d\) = maximum distance for proper communication
• \(h_1\) = height of the first antenna
• \(h_2\) = height of the second antenna
• \(R\) = radius of the Earth, approximately \(6,371 \, \text{km}\)

Given:

• \(h_1 = 245 \, \text{m}\)
• \(h_2 = 180 \, \text{m}\)

Convert heights from meters to kilometers:

• \(h_1 = 0.245 \, \text{km}\)
• \(h_2 = 0.180 \, \text{km}\)

Substitute the values into the formula:

\(d = \sqrt{2 \cdot 0.245 \cdot 6,371} + \sqrt{2 \cdot 0.180 \cdot 6,371}\)

Calculate each term separately:

• \(\sqrt{2 \cdot 0.245 \cdot 6,371} \approx \sqrt{3,121.07} \approx 55.84 \, \text{km}\)
• \(\sqrt{2 \cdot 0.180 \cdot 6,371} \approx \sqrt{2,295.96} \approx 47.96 \, \text{km}\)

Add the two results to find the maximum distance:

\(d = 55.84 + 47.96 \approx 103.8 \, \text{km}\)

Rounding to the nearest whole number, the maximum distance is approximately 104 km.

Thus, the correct answer is 104 km, which matches the given correct answer.