The distance d in Km to the gorizon can be estomated using the formula d= rootover13h, where h is the height above ground level, in meters of the observer.
a)use the formula to find the distance to the horizon for an observer on the london eye, 135m above ground.
b)rearrange the formula to make h the subject.
To determine how far in miles we can see from the top of a building of height h ft., we use d = sqrt[1.5h].
Using your expression of d = sqrt(13h), d in km and h in meters,
d = sqrt[13h) = sqrt[13(135)] = 41.89km.
= 25.97 miles
Using my expression, d = sqrt(1.5h), d in miles and h in feet,
d = sqrt[1.5(135)3.281] = 25.77 miles
a) To find the distance to the horizon for an observer on the London Eye, 135m above ground, we can use the formula:
d = √(13h)
Substituting the given height, h = 135m, into the formula:
d = √(13 * 135)
We can calculate the value of d using a calculator or by simplifying:
d ≈ √(1755) ≈ 41.95 km
Therefore, the approximate distance to the horizon for an observer on the London Eye is 41.95 km.
b) To rearrange the formula and make h the subject, we need to isolate h on one side of the equation:
d = √(13h)
First, square both sides of the equation:
(d)^2 = (√(13h))^2
d^2 = 13h
Next, divide both sides of the equation by 13:
d^2 / 13 = (13h) / 13
h = d^2 / 13
Therefore, the formula rearranged to make h the subject is:
h = d^2 / 13
a) To find the distance to the horizon for an observer on the London Eye, who is 135m above the ground, we can use the given formula:
d = √(13h)
Let's substitute h = 135m into the formula:
d = √(13 * 135)
d = √(1755)
d ≈ 41.9 km
Therefore, the distance to the horizon for an observer on the London Eye, 135m above the ground, is approximately 41.9 km.
b) To rearrange the formula to make h the subject, we need to isolate h on one side of the equation. Start with the given formula:
d = √(13h)
To get rid of the square root, we square both sides of the equation:
d^2 = (√(13h))^2
d^2 = 13h
Now, to isolate h, we divide both sides of the equation by 13:
h = d^2 / 13
Thus, the formula rearranged to make h the subject is:
h = d^2 / 13