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Alex787
2 months ago
10

Level curves for barometric pressure (in millibars) are shown for 6:00 AM on November 10, 1998. A deep low with pressure 972 mb

is moving over northeast Iowa. The distance along the red line from K (Kearney, Nebraska) to S (Sioux City, Iowa) is 300 km. Estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City.
Mathematics
1 answer:
AnnZ [12.3K]2 months ago
7 0

Answer: the directional derivative value of the pressure function at Kearney moving toward Sioux City is - 0.09 mb/km

Step-by-step explanation:

Let’s assume P represents the pressure function

The calculation for the directional derivative of pressure at Kearney directed towards Sioux City will be denoted as DuP

The line connecting Kearney to Sioux City starts on the level curve representing a pressure of 1000mb

and ends on the level curve representing a pressure of 972 mb

thus letting X1 = 1000 mb

X2 = 972 mb

the distance between Kearney and Sioux is d = 300 km

So to approximate the directional derivative DuP at Kearney towards Sioux City, we assess the average rate of pressure change between both locations

therefore DuP  = (X2 - X1) / d

= (972 - 1000) / 300

= -28 / 300

= - 0.09 mb/km

Thus, the directional derivative value of the pressure function at Kearney in the direction of Sioux City is - 0.09 mb/km

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