The range of a 100 meter high T.V. transmitter Ariel is about ________?
- 10 km
- 50 km
- 36 km
- 20 km
Explanation
To find the range (d) of a TV transmitter antenna, we use the line-of-sight formula:
d ≈ √(2 × h × R)
Where:
- d = distance to the horizon in kilometers
- h = height of the antenna in kilometers
- R = radius of Earth ≈ 6371 km
Convert height:
h = 100 m = 0.1 km
Now plug in:
d ≈ √(2 × 0.1 × 6371) ≈ √1274.2 ≈ 35.7 km
So, the range is approximately 36 km
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