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Question

The maximum distance up to which TV transmission from a TV tower of height h can be received is proportional to


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Solution

Step 1: Given data

The height of the TV tower is h.

Step 2: Solution

We need to calculate the maximum distance the signals travel from the tower considering the fact that the surface of the earth is curved.

Step 3: Construct the conditions using the fact the earth is curved

AO is the radius of the earth R

AB is the maximum distance the signal can travel, let it be D

We can clearly see OB=h+R

And we can observe OAB=90°

Step 4: Using Pythagoras's theorem

From Pythagoras theorem OB2=OA2+AB2

(h+R)2=d2+R2

d2=h2+R2+2Rh-R2

d2=h2+2Rh

As R>>h we can neglect h2

d2=2hR

d=2hR

⇒ The maximum distance the signals travel is d=2hR

Now, we can easily see that dh.

Thus the maximum distance up to which TV transmission from a TV tower of height h can be received is proportional to the square root of h.


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