Question

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

• A. 200 m
• B. 300 m
• C. 600 m
• D. 900 m

Answer 1

The Correct Option is D

To determine the new height required for the TV transmission tower to triple its coverage range, we need to understand how the coverage range of a tower is related to its height.

The coverage range (\(R\)) of a transmission tower is given by the following formula:

\(R = \sqrt{2 \times h \times R_E}\)

Where:

• \(h\) is the height of the tower.
• \(R_E\) is the radius of the Earth, approximately 6400 km (or 6,400,000 m).

To triple the coverage range, the new range \(R_{\text{new}}\) should be:

\(R_{\text{new}} = 3 \times R\)

This implies:

\(\sqrt{2 \times h_{\text{new}} \times R_E} = 3 \times \sqrt{2 \times h \times R_E}\)

By squaring both sides, we get:

\(2 \times h_{\text{new}} \times R_E = 9 \times (2 \times h \times R_E)\)

This simplifies to:

\(h_{\text{new}} = 9 \times h\)

Given the original height \(h = 100 \, \text{m}\), the new height \(h_{\text{new}}\\) should be:

\(h_{\text{new}} = 9 \times 100 \, \text{m} = 900 \, \text{m}\)

Therefore, the height of the tower should be increased to 900 m to triple its coverage range.

Thus, the correct answer is: 900 m.