Question 475353: So I need some help on this problem. I got part of it done and just need to know if it's right. I really need a good grade on this. Thanks so much for the help.
2. The equation [D=1.2sqrt(h)] gives the distance (D) in miles that a person can see to the horizon from a height (h) in feet.
2A) Solve this equation for h. [I got h=(D/1.2)squared.]
2B) Pike’s Peak, towering above Colorado Springs, Colorado is 14, 110 feet in elevation. How far can you see to the horizon from the top of Pike’s Peak? Round distance to nearest tenth of a mile.
2C) Can you see Denver, Colorado which is about 70 miles away? Show all work to explain your answer.
2D) Mt. McKinley, in Denali National Park in Alaska, is 20,320 feet above Sea Level. From the top of Mt. McKinley, could you see Fairbanks, some 120 miles away? Show all work to explain your answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is:
D = 1.2 * sqrt(h)
D is in miles
h is in feet.
Solving this equation for h, you get:
h =(D/1.2)^2
you are correct on that.
In 2B, h = 14110 which means you can see 1.2 * sqrt(14110) = 142.5 miles.
If you want to test your formula for h, then use that formula to get back to the height given the distance.
That formula becomes:
h = (D/1.2)^2 which becomes (142.5426252/1.2)^2 which becomes 14110.
In 2C, you are asked if you can see Denver, presumably from Pike's Peak. Since you can see 142.5 miles to the horizon from Pike's Peak, then you should have no problem seeing Denver which is only 70 miles away.
In 2D, you are given that h = 20320.
plug that in you equation for D and you get D = 1.2 * sqrt(20320) which equals 171.0578849 miles which rounds to 171 miles.
Since 171 miles is greater than 120 miles, you should easily be able to see Fairbanks which is only 120 miles away.
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