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.

Question

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.

Answer 1

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