We begin with the assumption that will travel left as increases. This gives us

a) In order to deduce that , we first note that must lie on the trajectory, from which it follows that . We then remember that when the plane lands, , allowing us to solve a quadratic equation to prove that .

b) Knowing that Captain Sullenberger flies left at speed , we may deduce that . Here is a hint to prove that : we may use the fact that .

c) Here, we may use the Chain Rule, , together with the fact that .

One final note: this problem is made tricky by the fact that can be considered either a function of or a function of . The notation is therefore ambiguous, as it could refer to the value of when (which is ) or when (which is ).