2. The D = 1.2(sqrt)h equation 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. Long’s Peak in the Rocky Mountain National Park, is 14,255 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.
Cutting and pasting questions usually does not work
a. To solve the equation D = 1.2(sqrt)h for h, we need to isolate the variable h.
Starting with the equation: D = 1.2(sqrt)h
Step 1: To eliminate the square root, square both sides of the equation:
D^2 = (1.2(sqrt)h)^2
D^2 = 1.44h
Step 2: Divide both sides of the equation by 1.44:
(D^2) / 1.44 = h
Therefore, the equation solved for h is h = (D^2) / 1.44.
b. Now let's use the equation h = (D^2) / 1.44 to find out how far you can see to the horizon from the top of Long's Peak.
Given:
Height, h = 14,255 feet
Using the equation, we have:
D = 1.2(sqrt)h
D = 1.2(sqrt)14,255
D = 1.2 * sqrt(14,255)
D ≈ 1.2 * 119.452
D ≈ 143.34 miles
So, you can see approximately 143.34 miles to the horizon from the top of Long's Peak.
To determine if you can see Cheyenne, Wyoming (about 89 miles away), we compare the distance to the horizon (143.34 miles) with the distance to Cheyenne (89 miles).
Since the distance to Cheyenne (89 miles) is less than the distance to the horizon (143.34 miles), it means that you can see Cheyenne from the top of Long's Peak.