Question

The arch beneath a bridge is semi-elliptical , a one-way roadway passes under the arch. The width of the roadway is 30 feet and the height over the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 13 feet and truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and determine which truck can pass under the bridge?A) truck 1 can pass under the bridge,but truck 2 can not.B) both truck 1 and truck 2 can pass under the bridge.C) truck 2 can pass under the bridge, but truck 1 can not.D) neither truck 1 nor truck 2 can pass under the bridge.

Answer 1

They both can pass, if they pass 1 at the time

Step-by-step explanation:

The equation of the semi-elliptical arc is:

`(x^2)/(15^2) +(y^2)/(14^2)=1`

`y=+14*\sqrt{1-(x^2)/(15^2)}`

We need to know the hight (y) at x=4feet (half the width of the truck):

y = 13.49 feet

Since the height of the arc at that point is greater than the height of both trucks, we conclude that they can both pass