Solve the problem.
-The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use
This road. They are both 12 feet wide. Truck 1 has an overall height of 13 feet and Truck 2 has an overall height
Of 14 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.
A)Neither Truck 1 nor Truck 2 can pass under the bridge.
B)Truck 1 can pass under the bridge, but Truck 2 cannot.
C)Truck 2 can pass under the bridge, but Truck 1 cannot.
D)Both Truck 1 and Truck 2 can pass under the bridge.

Question

Quizplus · Accepted Answer

The semi-elliptical arch can be described by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the width of the roadway (38 feet) and $2b$ is the height of the arch (28 feet, since it's semi-elliptical and the height given is 14 feet). The trucks, being 12 feet wide, will not be at the center of the arch but rather closer to its edges where the height is less than 14 feet. Truck 1, being 13 feet tall, can pass because the height of the arch at the points directly above the edges of the truck will be greater than 13 feet. Truck 2, being 14 feet tall, might not have enough clearance due to the curvature of the arch reducing height towards the edges. Therefore, only Truck 1 can safely pass under the bridge.

Solve the Problem. -The Arch Beneath a Bridge Is Semi-Elliptical, a One-Way Roadway