The equation D=1.2times square root h gives the distance, D, in miles a person can see to the horizon from a height, h, in feet.
a. sovle for h.
b. Long's Peak is 14,255 feet in elevation. How far can you see to the horizon for Long's Peak? Can you see Cheyenne, Wyoming (about 89 miles away)? Explain .
I think for part a. that h=D^2 divided by 1.44 is this correct? How do I set up the next part? I'm confused on setting it up.
To solve for h in the equation D = 1.2 * √h, we can follow these steps:
a. Solve for h:
Step 1: Divide both sides of the equation by 1.2: D/1.2 = √h
Step 2: Square both sides of the equation: (D/1.2)^2 = (√h)^2
Step 3: Simplify both sides: D^2 / (1.2)^2 = h
Step 4: Simplify the denominator on the right side: D^2 / 1.44 = h
So, your solution h = D^2 / 1.44 is correct.
b. Now, we can calculate how far you can see to the horizon from Long's Peak. Given that the elevation of Long's Peak is 14,255 feet, we need to substitute this value into the equation to calculate D, the distance to the horizon.
Step 1: Substitute the value of h into the equation:
D = 1.2 * √(14,255)
Step 2: Evaluate the square root:
D = 1.2 * 119.5
D = 143.4 miles
Therefore, you can see approximately 143.4 miles to the horizon from Long's Peak.
To determine if you can see Cheyenne, Wyoming (about 89 miles away), you compare the distance to the horizon with the distance to Cheyenne:
Since the distance to Cheyenne is within the range of the distance to the horizon, it is possible to see Cheyenne from Long's Peak.