Step 5: Use the shifted form of the quadratic equation found in Step 3 to determ

Question

Step 5: Use the shifted form of the quadratic equation found in Step 3 to determine how high
above the High Water Level the crown of the Main Arch is.
Step 3-->

How does this compare
to the actual value shown in the sketch?

Step 6: Use shifted form found in Step 3 and the sketch to determine how high the crown of the
Main Arch is above the road. How does this compare to the actual height found using
the numbers in the sketch?

Step 7: If you are walking on the bridge and stop after you have traveled 35% of the way from
the left pin, how high above the road is the Main Arch?

Step 8: Suppose you are in a row boat and stop to fish about 62% of the way from the left pin,
how high above you is the Main Arch?

Explanation / Answer

Step 5:

From the diagram, we can see that Main Arch is allocated at almost 2/9 part of the total length. Therefore, the distance of the foot of main arch from left pin would be (2/9)*531 = 118 feet.

Hence, Height of Main Arch = 21.0762+1.3289*118-0.0027*(118)^2

Height of main arch = 140.29 feet

It is not very close to the actual height of the main arch.

Step 6:

Height of main arch using shifted model = 108.9626+0.0531*118

Height of the main arch using shifted model = 115.2284 feet.

It is very close to the actual height of the main arch.

Step 7:

First of all we find 35% of 531 feet, which is equal to 186.85.

Therefore,

21.0762+1.3289*185.85-0.0027*(185.65)^2 - 64 = 175-64 = 111 feet.

Hence, the Main Arch is 111 feet above the road.

Step 8:

62 % for way is 329.22 feet.

Therefore,

21.0762+1.3289*329.22-0.0027*(329.22)^2 - 64 = 165-64 = 101 feet.

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