The equation D=1.2(SQRT)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. 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.
A. If D = 1.2 sqrtH, then
D^2 = 1.44 H
Solve that equation for H by dividing both sides by 1.44.
B. Plug in 14255 for H. Take the square root and multiply by 1.2. You should be able to perform those calculations. Compare the horizon distance you get to 89 miles.
A. To solve the equation D = 1.2 √H for h, we need to isolate the variable h.
Step 1: Start with the equation D = 1.2 √H.
Step 2: Divide both sides of the equation by 1.2: D/1.2 = √H.
Step 3: Square both sides of the equation to eliminate the square root: (D/1.2)^2 = H.
Step 4: Simplify the equation: H = (D^2) / 1.44.
Therefore, the equation h = (D^2) / 1.44 represents the solution for h.
B. Given that Long's Peak has an elevation of 14,255 feet, we can use the formula D = 1.2 √H to find out the distance you can see to the horizon from the top of Long's Peak.
Step 1: Substitute H = 14,255 into the equation: D = 1.2 √14,255.
Step 2: Calculate the square root of 14,255: √14,255 ≈ 119.47.
Step 3: Multiply 1.2 by the square root result: 1.2 * 119.47 ≈ 143.36.
Therefore, from the top of Long's Peak, you can see approximately 143.36 miles to the horizon.
Regarding Cheyenne, Wyoming, which is about 89 miles away from Long's Peak, you cannot see it from the top. This is because the distance to the horizon from Long's Peak is greater than 89 miles. Since the equation gives the distance to the horizon, and the distance to Cheyenne is less than the distance to the horizon, it means Cheyenne, Wyoming is not visible from the top of Long's Peak.