Gladesville Bridge 2

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This question is a variation on another version which asks the student to find the height of a bridge arch and width of the river given a formula for the arch of the bridge (also available in the Numbas database)

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Don Shearman

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Don Shearman 9 months ago

Published this.

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Don Shearman 1 year, 11 months ago

Created this.

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Question statement

The following question was proposed to Chat GPT (the above image is for reference and was not provided to ChatGPT):

The Gladesville Bridge is an arch bridge which spans the Parramatta River near Sydney. The bottom of the arch of the bridge can be modeled by the equation

$y=\frac{180}{305}x(1-\frac{1}{305}x)$ where

$y$ is the height of the arch above the water line in metres and

$x$ is the horizontal distance from the left bank of the river in metres. What is the width of the river?

The response was:

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To find the width of the river, we need to find the distance between the left bank and the right bank of the river. Since the bridge spans the river, the distance between the left and right banks is equal to the length of the arch.

The equation given for the arch of the bridge is:

$y=\frac{180}{305}x(1-\frac{1}{305}x)$

that makes sense in the context of the problem. Looking at a map of the area, we can see that the Gladesville Bridge is the only bridge that spans the Parramatta River at Gladesville, so the length of the arch must be less than the distance between the two nearest points on the riverbanks where the bridge can be anchored.

From the map, we can estimate that the distance between these two points is approximately 260 meters.

Is the value obtained by ChatGPT correct for the information supplied to it?

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Support your conclusion mathematically in your handwritten notes using the equation of the arch.

Advice

No, the distance stated by ChatGPT is not an accurate representation of the river. From the photo in the question we can see that the lower arch of the bridge just touches each side of the river. Given that the formul for the arch is

$y=\frac{180}{305}x(1-\frac{1}{305}x)$ where

$y$ is the height of the arch above the water line in metres we can see that the arch will touch the water line

$y=0$ when

$x=0$ metres (the left side of the bridge in the photo), or

$x=305$ metres. hence the width of the river is

$305$ metres.

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This question is used in the following exam:

Class Test 2 by Don Shearman in MfEP Progress Quizzes.

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Taxonomy: mathcentre

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Don Shearman 9 months ago

Don Shearman 1 year, 11 months ago

Error in variable testing condition

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