Precalculus (6th Edition) Blitzer

Step 1. Using the given figure, set the vertex of the arch as the origin. We can write the general form of the equation for the parabola as $x^2=4py$ Step 2. As point $(100,-50)$ is on the curve, we have $100^2=4p(-50)$, which gives $p=-50$ Step 3. At 30 feet from the center, we have $x=30$. Thus $y=\frac{x^2}{4p}=\frac{30^2}{4(-50)}\approx-4.5$, which means that at $x=30$, the arch is $50-4.5=45.5\ ft$ from the water and the boat (30 feet high) is clear to pass.