The height of a T. V. tower is 100 m. If radius of earth is 6400 km,then what is the maximum distance of transmission from it

To solve this problem, we need to use the formula for the line of sight distance or the horizon distance. This is the maximum distance at which an observer can see an object on the earth's surface. The formula is:

d = √(2rh + h²)

where:

• d is the line of sight distance,
• r is the radius of the earth, and
• h is the height of the object.

Given that the radius of the earth (r) is 6400 km or 6400000 m and the height of the TV tower (h) is 100 m, we can substitute these values into the formula:

d = √(2 * 6400000 m * 100 m + (100 m)²) d = √(1280000000 m² + 10000 m²) d = √1280010000 m² d ≈ 35786.16 m

Therefore, the maximum distance of transmission from the TV tower is approximately 35786.16 m or 35.78616 km.