The distance d in kilometres to the horizon can be estimated using the formula d = root13h,where h is the height above ground level, in metres, 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.
Now wait a minute, try this yourself first. I already know how to do it and have already done two of these for you.
(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 h = 135m into the formula, we have:
d = √13 * 135
Calculating this expression, we get:
d ≈ √(1755) ≈ 41.9 km
Therefore, the distance to the horizon for an observer on the London Eye is approximately 41.9 kilometers.
(b) To rearrange the formula to make h the subject, we start with the equation d = √13h.
First, square both sides of the equation to eliminate the square root:
d^2 = 13h
Next, divide both sides of the equation by 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 ground, we can use the formula d = √13h, where h is the height above ground level. Substituting the given value of h = 135m into the formula, we get:
d = √13 * 135
Now, let's calculate the value of d:
d ≈ √13 * 135
d ≈ √(13 * 135)
d ≈ √(1755)
d ≈ 41.91 km
Therefore, the distance to the horizon for an observer on the London Eye, who is 135m above ground, is approximately 41.91 kilometers.
(b) To rearrange the formula to make h the subject, we need to isolate h on one side of the equation. The formula is:
d = √13h
To make h the subject, we can start by squaring both sides of the equation to eliminate the square root:
d^2 = (√13h)^2
d^2 = 13h
Now, divide both sides of the equation by 13 to solve for h:
h = d^2 / 13
So, the rearranged formula to make h the subject is h = d^2 / 13.