Question

1. (10 pts) The formula for calculating the distance, d, in miles that one can see to the horizon on aclear day is approximated by d = 1.22√x, where x, is the elevation in feet of a person's eyes.a. Approximate how far in miles can a person whose eyes are 5' 6" from the ground see tothe horizon when they are at sea-level. (Hint: Height is often measured with two units,feet and inches, but this formula does not allow for two units.) Figure out if you need toconvert to feet or inches and then do the conversion out as a multiplication problembefore you answer the question Round to the nearest hundredth if necessary.b. How far does the same person see when they are standing on top of an 8,000 footmountain? (Hint: Consider where are their eyes if the mountain is the given height)Round to the nearest hundredth if necessary.

Answer 1

`\begin{gathered} a)2.86\:miles \\ b)109.12\:miles \end{gathered}`

1) We need to use one single unit to express the elevation of a person's eyes.

a)

`5^(\prime)6`

Remember that 1 foot is equal to 12 inches. And dividing 66" by 12 yields 5.5'

Now, let's plug into the formula we've been given:

`d=1.22√(5.5)\Rightarrow d=2.86\:miles`

b) Now, let's bear in mind that this same person has reached the top of a mountain, and now he's at 8,000 feet high:

`d=1.22√(8000)\Rightarrow d=109.12\:miles`

Note that x, is always given in feet, as well as, d is in miles.