2. The equation D=2.2√ h gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
b. If Long’s Peak in Rocky Mountain National Park, is 14,275 feet in elevation, how far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)? Explain your answer.
square both sides
D^2/4.84 = h
b)
D = 2.2√14275 = 262.9 miles ??
BTW. I always thought that in the old system
D = 1.2246√h
a. To solve the equation D=2.2√ h for h, we need to isolate the variable h.
1. Start with the equation D = 2.2√ h.
2. Divide both sides of the equation by 2.2: D/2.2 = √ h.
3. To eliminate the square root, square both sides of the equation: (D/2.2)^2 = (√ h)^2.
4. Simplify: D^2 / 2.2^2 = h.
5. Final answer: h = D^2 / 2.2^2.
b. To find out how far you can see to the horizon from the top of Long’s Peak, we can use the equation we derived in part a.
1. Substitute the given elevation, h = 14,275 feet, into the equation: D = 2.2√(14,275).
2. Calculate the square root of 14,275: √(14,275) ≈ 119.5.
3. Multiply the result by 2.2: D ≈ 2.2 * 119.5 ≈ 263.9 miles.
Therefore, from the top of Long’s Peak, you can see approximately 263.9 miles to the horizon.
As for whether you can see Cheyenne, Wyoming, which is approximately 89 miles away, the answer depends on the curvature of the Earth. Generally, the Earth's surface curves away from our line of sight, limiting long-distance visibility.
Assuming a flat terrain, since 263.9 miles is greater than 89 miles, it is theoretically possible to see Cheyenne from the top of Long’s Peak. However, factors such as atmospheric conditions, obstructions, and the individual's height above the ground may affect visibility.
Keep in mind that this calculation assumes ideal conditions and a perfectly flat terrain, so the actual visibility may vary.