The equation given, D(h) = 111.7 / h, suggests an inverse relationship between the distance D(h) and the height h. However, as previously clarified, this relationship is not physically accurate, as one would expect to see farther as they climb higher, not less distance. But, if we take this equation at face value and solve for the height that would allow a person to see exactly 30 kilometers, we can proceed as follows.
Given the equation D(h) = 111.7 / h and the condition D(h) = 30 kilometers, we want to find the value of h that satisfies this condition.
To solve for h, we set the distance D(h) equal to 30 kilometers:
30 = 111.7 / h.
Now, we can isolate h by multiplying both sides of the equation by h and then dividing both sides by 30:
h * 30 = 111.7,
h = 111.7 / 30.
Now we can perform the division to find the value of h:
h ≈ 3.723333333.
Rounding the answer to two decimal places gives:
h ≈ 3.72 kilometers.
So, according to the given equation, a height of approximately 3.72 kilometers would be required for a person to see 30 kilometers. Remember that this outcome is based on an incorrect physical interpretation implied by the given equation D(h) = 111.7 / h.
