How Far Can A Person See?

In summary, the distance a person can see is influenced by several factors, including the curvature of the Earth, atmospheric conditions, and the observer's height above sea level. On flat terrain, the average person can see about 3 miles (4.8 kilometers) to the horizon. However, this distance increases with elevation; for example, from a height of 100 feet, one can see approximately 12 miles (19 kilometers). Additionally, visibility can be affected by weather conditions, such as fog or haze, which may limit how far one can see.
  • #1
felizgu
17
8
Homework Statement
How far can a person see standing on the observation deck?
Relevant Equations
Pythygorean Theorem
The tallest building in the world is Burj Khalifa in Dubai, United Arab Emirates, at 2717 feet and 160 floors.The observation deck is 1450 feet above ground level. How far can a person standing on the observation deck see (with the aid of a telescope)? Use 3960 miles for the radius of Earth.

Let me see. I know that the Pythygorean Theorem is needed.

Let s = how far a person can see.

Let d = height of observation deck.

Let r = radius of Earth

Let m = number of feet in a mile

I think the correct expression of the Pythagorean Theorem for this problem is the following:

s^2 + r^2 = [ r + (d/m)]^2

I will now replace the letters with the value for each. I need to solve for s.

(s)^2 + (3690)^2 = [3960 + (1450/5280)]^2

Is this the correct set up?
 
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  • #2
It looks correct.

I would recommend solving the initial equation symbolically first and only then insert the numbers to calculate the actual value.
 
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Thread closed due to OP being banned for creating multiple accounts.
 

FAQ: How Far Can A Person See?

1. What factors affect how far a person can see?

Several factors influence how far a person can see, including the curvature of the Earth, atmospheric conditions (like humidity and pollution), the observer's height above sea level, and the presence of obstacles such as buildings or trees. Generally, a person's height increases the distance they can see over the horizon.

2. How does height affect visibility distance?

Height significantly impacts visibility distance due to the curvature of the Earth. The formula to estimate the distance to the horizon in miles is approximately the square root of the observer's height in feet. For example, a person standing at a height of 6 feet can see about 3 miles to the horizon.

3. Can atmospheric conditions enhance visibility?

Yes, atmospheric conditions can enhance visibility. Clear, dry air allows for better visibility than humid or polluted air. Additionally, temperature inversions can create optical phenomena that extend visibility, while fog, rain, or haze can significantly reduce it.

4. Is there a limit to how far a person can see with the naked eye?

While the naked eye can detect distant objects, there is a practical limit based on factors like light, contrast, and the size of the object. Under ideal conditions, a person can see up to about 10 to 12 miles away, but this is often limited by the Earth's curvature and obstacles.

5. How does light pollution affect visibility?

Light pollution can greatly affect visibility, particularly in urban areas. Excessive artificial light can wash out the night sky, making it difficult to see stars and other celestial objects. This phenomenon reduces the effective distance one can perceive in the night sky and can also affect visibility during twilight hours.

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