Question

The height of a TV tower is 180 m. To what distance the transmission can be made from this tower, if the radius of earth is \(6.4 \times 10^6\) m?

• A. 18 km
• B. 90 km
• C. 48 km
• D. 64 km

Hint:

The transmission distance depends on the height of the tower and the radius of the Earth. Use the formula \(d = \sqrt{2 \cdot h \cdot R}\) for such calculations.

Answer 1

The Correct Option is C

We use the formula for the transmission distance: \[ d = \sqrt{2 \cdot h \cdot R} \] Substitute the values: \[ d = \sqrt{2 \cdot 180 \cdot 6.4 \times 10^6}
d = \sqrt{2.304 \times 10^9}
d = 48 \times 10^3 \, \text{m} = 48 \, \text{km} \] Hence, the transmission distance is 48 km.