Question: Suppose you are trying to design a ramp so that a ball rolling down the ramp will reach the bottom as quickly as possible. The function giving the optimal shape must solve Euler's equation:

\(\frac{\partial L}{\partial y}=\frac{d}{d x} \frac{\partial L}{\partial y}\)

where \(L\) is defined as follows:

\(L\left(x, y, y^{\prime}\right)=\sqrt{\frac{1+y^{\prime 2}}{-2 g x}}\)

Solve for \(y\).

Price: $2.99

Solution: The downloadable solution consists of 1 pages
Deliverable: Word Document