2. The equation D=1.2 square 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 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.
I have try to solve this problem in different ways and I still don't know how to do it.
d=1.2sqrt h
d^2/1.44= h
b. use the equation d=1.2sqrt(14,255)
about 143 miles
thank you very much, bobpursley. Now I can do the rest of my work.
a. To solve the equation D = 1.2 square h for h, we need to isolate h on one side of the equation.
The equation can be rewritten as:
D = 1.2h^2
To isolate h, divide both sides of the equation by 1.2:
D/1.2 = (1.2h^2)/1.2
This simplifies to:
D/1.2 = h^2
To find h, take the square root of both sides of the equation:
√(D/1.2) = √(h^2)
Simplifying further:
h = √(D/1.2)
Now you have a formula to solve for h.
b. To find the distance D that a person can see to the horizon from the top of Long’s Peak (which has a height of 14,255 feet), we can substitute this value into the equation h = √(D/1.2) and solve for D.
Plugging in h = 14,255 into the equation, we get:
14,255 = √(D/1.2)
Square both sides of the equation to eliminate the square root:
14,255^2 = (D/1.2)
Simplify the equation:
D/1.2 = 14,255^2
Multiply both sides of the equation by 1.2 to isolate D:
D = 1.2 * 14,255^2
Now you can calculate the value of D to find the distance you can see to the horizon from the top of Long’s Peak.
To determine if you can see Cheyenne, Wyoming (about 89 miles away), you compare the calculated distance D to the actual distance. If the calculated distance D is greater than or equal to the actual distance (89 miles), then you would be able to see Cheyenne. Otherwise, you would not be able to see it.
Plug in the value for D and compare it with the actual distance of 89 miles. If D is greater than or equal to 89 miles, you can see Cheyenne; otherwise, you cannot.
By following these steps, you should be able to solve the problem and determine whether or not you can see Cheyenne from the top of Long’s Peak.