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 12 feet. Two trucks plan to use
This road. They are both 8 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of
10 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.
A)Both Truck 1 and 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)Neither Truck 1 nor 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 arch (38 feet) and $2b$ is the height of the arch (24 feet, but since it's semi-elliptical, we use 12 feet for $b$). Given the dimensions, both trucks being 8 feet wide will not affect their ability to pass side by side under the 38 feet wide arch. The critical factor is their height. Since the arch's maximum height is 12 feet at the center and both trucks are shorter than this (11 feet and 10 feet), both trucks can pass under the bridge without any height restrictions.

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