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

Options

A. `h^(1//2)`
B. h
C. h
D. `h^(2)`

Answer

To solve the problem of determining the proportionality of the maximum distance up to which TV transmission from a TV tower of height \( h \) can be received, we can follow these steps:

### Step 1: Understand the relationship between height and distance
The maximum distance \( d \) (or radius \( R \)) from which a TV signal can be received is influenced by the height of the TV tower \( h \). This relationship is derived from the geometry of the Earth and the line of sight.

### Step 2: Use the formula for maximum distance
The formula for the maximum distance \( d \) that can be received from a tower is given by:
\[ d = \sqrt{2 \cdot h \cdot R} \]
where \( R \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \) meters).

### Step 3: Identify the proportionality
From the formula, we can see that the distance \( d \) is proportional to the square root of the height \( h \):
\[ d \propto \sqrt{h} \]
This means that if we increase the height of the tower, the distance over which the signal can be received increases with the square root of that height.

### Step 4: Conclude the proportionality
Thus, we can conclude that the maximum distance \( d \) up to which TV transmission can be received is proportional to \( h^{1/2} \) or \( \sqrt{h} \).

### Final Answer
The maximum distance up to which TV transmission from a TV tower of height \( h \) can be received is proportional to \( h^{1/2} \).

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