A concrete bridge is designed as a parabolic arch. The road over bridge is 40 m long and the maximum height of

Question 104 of 126

Q. A concrete bridge is designed as a parabolic arch. The road over bridge is 40 m long and the maximum height of the arch is 15 m. Write the equation of the parabolic arch. Take (0, 0) as the vertex.

Puducherry TnboardTamil Nadu HSC (DGE) Board 2020Subjective· 3mImportance★★★★★

83% · 104/126 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Models the arch as a downward-opening parabola with vertex at the origin, then uses the given span and height to find the parameter.

Since the vertex $(0,0)$ is taken at the topmost point of the arch and the arch curves downward on both sides, the equation has the standard form $x^2=-4ay$ (a downward-opening parabola with vertex at the origin), $a>0$ .
The road is 40 m long (the full span at road level) and the arch's maximum height is 15 m, so road level is $15$ m below the vertex, i.e. at $y=-15$ , and by symmetry the span there runs from $x=-20$ to $x=20$ . …

Q.A concrete bridge is designed as a parabolic arch. The road over bridge is 40 m long and the maximum height of the arch is 15 m. Write the equation of the parabolic arch. Take (0, 0) as the vertex.