Question

The height of the antenna is 98 m. The radius of Earth is 6400 km. The area up to which it will transmit signal is:

• A. 3642 km²
• B. 3942 km²
• C. 11200 km²
• D. 22400 km²

Hint:

For line-of-sight calculations, use the approximate formula d = √2Rh.

Answer 1

The Correct Option is B

To determine the area up to which the antenna will transmit the signal, we need to calculate the area of the circle on the surface of the Earth that the antenna can cover. This is done using the formula:

\(A = \pi \cdot d^2\)

Where \(d\) is the distance from the top of the antenna to the horizon as seen from that point.

The distance \(d\) can be found using the formula:

\(d = \sqrt{2 \cdot h \cdot R}\)

Where:

• \(h\) is the height of the antenna (\(98 \, \text{m} = 0.098 \, \text{km}\))
• \(R\) is the radius of the Earth (\(6400 \, \text{km}\))

Let's calculate \(d\):

\(d = \sqrt{2 \cdot 0.098 \cdot 6400}\)

\(d = \sqrt{1254.4}\)

\(d \approx 35.41 \, \text{km}\)

Now, we calculate the area \(A\) up to which the signal will transmit:

\(A = \pi \cdot (35.41)^2\)

\(A \approx 3.1416 \cdot 1254.4881\)

\(A \approx 3942 \, \text{km}^2\)

Therefore, the area up to which the antenna will transmit the signal is approximately \(3942 \, \text{km}^2\), which matches the provided correct answer.