Question

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21% ?

• A. 12%
• B. 15%
• C. 14%
• D. 10%

Answer 1

The Correct Option is D

TV Tower Transmission Range Problem 

Step 1: Transmission Range Formula

The transmission range (\( d \)) of a TV tower is given by:

\( d = \sqrt{2Rh} \)

where \( R \) is the radius of the Earth and \( h \) is the height of the tower.

Step 2: New Height

If the height is increased by 21%, the new height (\( h' \)) is:

\( h' = h + 0.21h = 1.21h \)

Step 3: New Transmission Range

The new transmission range (\( d' \)) is:

\( d' = \sqrt{2Rh'} = \sqrt{2R(1.21h)} = \sqrt{1.21} \sqrt{2Rh} = 1.1\sqrt{2Rh} \)

Step 4: Percentage Increase

Since \( d = \sqrt{2Rh} \), the new range is:

\( d' = 1.1d \)

The percentage increase in the transmission range is:

\( \frac{d' - d}{d} \times 100 = \frac{1.1d - d}{d} \times 100 = 0.1 \times 100 = 10\% \)

Conclusion:

The transmission range increases by 10% (Option 4).