Kaylib's Eye-level Height Is 48 Ft Above Sea Level, And Addison's Eye-level Height Is $85 \frac{1}{3} \text{ Ft}$ Above Sea Level. How Much Farther Can Addison See To The Horizon? Use The Formula $d = \sqrt{\frac{3h}{2}}$, Where

Introduction

When it comes to determining the distance one can see to the horizon, several factors come into play, including the observer's eye-level height and the curvature of the Earth. In this article, we will explore how to calculate the horizon distance using the given formula and apply it to two different scenarios: Kaylib's eye-level height of 48 ft above sea level and Addison's eye-level height of $85 \frac{1}{3} \text{ ft}$ above sea level.

Understanding the Formula

The formula to calculate the horizon distance is given by:

$$d = \sqrt{\frac{3h}{2}}$$

where $d$ is the distance to the horizon and $h$ is the observer's eye-level height above sea level.

Calculating the Horizon Distance for Kaylib

To calculate the horizon distance for Kaylib, we need to substitute his eye-level height into the formula.

• Kaylib's Eye-Level Height: 48 ft
• Formula: $d = \sqrt{\frac{3h}{2}}$

Substituting Kaylib's eye-level height into the formula, we get:

$$d = \sqrt{\frac{3(48)}{2}}$$

Simplifying the expression, we get:

$$d = \sqrt{\frac{144}{2}}$$

$$d = \sqrt{72}$$

$$d = \sqrt{36 \times 2}$$

$$d = 6\sqrt{2}$$

$$d = 6 \times 1.414$$

$$d = 8.484$$

Therefore, Kaylib can see approximately 8.484 ft to the horizon.

Calculating the Horizon Distance for Addison

To calculate the horizon distance for Addison, we need to substitute her eye-level height into the formula.

• Addison's Eye-Level Height: $85 \frac{1}{3} \text{ ft}$
• Formula: $d = \sqrt{\frac{3h}{2}}$

First, we need to convert Addison's eye-level height to a decimal value.

$$85 \frac{1}{3} = 85 + \frac{1}{3}$$

$$85 \frac{1}{3} = 85 + 0.333$$

$$85 \frac{1}{3} = 85.333$$

Now, we can substitute Addison's eye-level height into the formula.

$$d = \sqrt{\frac{3(85.333)}{2}}$$

Simplifying the expression, we get:

$$d = \sqrt{\frac{256}{2}}$$

$$d = \sqrt{128}$$

$$d = \sqrt{64 \times 2}$$

$$d = 8\sqrt{2}$$

$$d = 8 \times 1.414$$

$$d = 11.312$$

Therefore, Addison can see approximately 11.312 ft to the horizon.

Comparing the Horizon Distances

Now that we have calculated the horizon distances for both Kaylib and Addison, we can compare the results.

• Kaylib's Horizon Distance: 8.484 ft
• Addison's Horizon Distance: 11.312 ft

As we can see, Addison can see approximately 2.828 ft farther to the horizon than Kaylib.

Conclusion

Introduction

In our previous article, we explored how to calculate the horizon distance using the given formula and applied it to two different scenarios: Kaylib's eye-level height of 48 ft above sea level and Addison's eye-level height of $85 \frac{1}{3} \text{ ft}$ above sea level. In this article, we will answer some frequently asked questions related to calculating the horizon distance.

Q&A

Q: What is the formula to calculate the horizon distance?

A: The formula to calculate the horizon distance is given by:

$$d = \sqrt{\frac{3h}{2}}$$

where $d$ is the distance to the horizon and $h$ is the observer's eye-level height above sea level.

Q: What is the significance of the observer's eye-level height in calculating the horizon distance?

A: The observer's eye-level height is a crucial factor in calculating the horizon distance. It determines how far one can see to the horizon. The higher the observer's eye-level height, the farther one can see to the horizon.

Q: Can I use the formula to calculate the horizon distance for any observer's eye-level height?

A: Yes, you can use the formula to calculate the horizon distance for any observer's eye-level height. Simply substitute the observer's eye-level height into the formula and solve for the distance to the horizon.

Q: What if the observer's eye-level height is not given in feet? Can I still use the formula?

A: Yes, you can still use the formula even if the observer's eye-level height is not given in feet. You can convert the observer's eye-level height to feet and then substitute it into the formula.

Q: Can I use the formula to calculate the horizon distance for observers at different locations?

A: Yes, you can use the formula to calculate the horizon distance for observers at different locations. However, you need to take into account the curvature of the Earth and the observer's eye-level height at each location.

Q: What is the maximum distance one can see to the horizon?

A: The maximum distance one can see to the horizon is determined by the Earth's curvature. The formula we used to calculate the horizon distance assumes a flat Earth, but in reality, the Earth is curved. Therefore, the actual distance one can see to the horizon is less than the calculated value.

Q: Can I use the formula to calculate the horizon distance for observers on a mountain or a hill?

A: Yes, you can use the formula to calculate the horizon distance for observers on a mountain or a hill. However, you need to take into account the observer's eye-level height above the mountain or hill.

Q: What if the observer's eye-level height is negative? Can I still use the formula?

A: No, you cannot use the formula if the observer's eye-level height is negative. The formula assumes a positive eye-level height, and a negative eye-level height would result in an imaginary distance.

Q: Can I use the formula to calculate the horizon distance for observers underwater?

A: No, you cannot use the formula to calculate the horizon distance for observers underwater. The formula assumes a flat surface, and underwater, the observer is surrounded by water, which affects the calculation of the horizon distance.

Conclusion

In conclusion, we have answered some frequently asked questions related to calculating the horizon distance. We hope this Q&A article has provided you with a better understanding of the formula and its limitations. If you have any further questions, please feel free to ask.