Question

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:
Given: Earth’s radius = \(6.4 \times 106\text{ m}\)

• A. 64 km
• B. 36 km
• C. 28 km
• D. 32 km

Hint:

For line of sight calculations:

• Use \[ d_\text{max} = \sqrt{2R h_t} + \sqrt{2R h_r}. \]
• Ensure consistent units for the Earth's radius and antenna height.

Answer 1

The Correct Option is A

1. Line of Sight Distance Formula: The maximum line of sight distance is: \[ d_{\text{max}} = \sqrt{2 R h_t} + \sqrt{2 R h_r}, \] where \( R = 6.4 \times 10^6 \, \text{m} \) (Earth's radius) and \( h_t = h_r = 80 \, \text{m} \).
2. Substitute Values: \[ d_{\text{max}} = \sqrt{2 \times 6.4 \times 10^6 \times 80} + \sqrt{2 \times 6.4 \times 10^6 \times 80}. \]
3. Simplify: \[ d_{\text{max}} = 2 \times \sqrt{1024000} = 2 \times 32 = 64 \, \text{km}. \]

Final Answer: \( \boxed{64 \, \text{km}} \)