Final answer:
None of the given answer choices correctly express Corey's distance to the east of the track's center in terms of the distance D, according to the information provided. The proper relationship appears to be h = D² / (2R), which is not listed among the options.
Step-by-step explanation:
To find the formula that expresses Corey's distance to the east of the track's center, we need to consider the context provided by the equations mentioned in the question. We're given an equation D = \(\sqrt{2Rh}\) that calculates D when h and R are known. This equation implies a relationship between the three quantities and suggests that D is derived from a geometric or physical context.
In one of the provided pieces of information, it is mentioned that D² = h(2R+h), which is close to the relationship we want to find, but rearranged. Given that R is much greater than h, the term h can be neglected, simplifying the equation to D² \approx h(2R). If we solve for h, we get h = \frac{D²} {2R}, which is not one of the provided options.
However, if we abide strictly by the options given in the question, none of the choices directly align with the rewritten equation h = \frac{D²} {2R}. Therefore, either more context is needed, or there might be an issue with the provided formula options. As per the options given, none of them correctly represent the relationship between h and D based on the information provided and the equation D² = h(2R+h).