Multiple choice

The maximum distance between the transmitting and receiving TV towers is $D$. If the heights of both transmitting and receiving towers are doubled, then the maximum distance between them becomes

  1. $2D$
  2. $\sqrt{2}D$
  3. $4D$
  4. $D/2$
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B Correct answer
Explanation

The distance D is proportional to the square root of the height (D is proportional to sqrt(h)). If heights are doubled, the new distance is proportional to sqrt(2h) = sqrt(2) * sqrt(h), which is sqrt(2) * D.

AI explanation

The maximum line of sight distance between a transmitting and a receiving TV tower is given by the formula D equals the square root of two times R times h, where R is the radius of the earth and h is the height of the towers. When the heights of both towers are doubled, the new distance becomes the square root of two times R times two h, which simplifies to the square root of two times the square root of two R h. By substituting the original distance D, the new maximum distance is the square root of two times D.

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