Meteorologists often measure the intensity of a tropical storm or hurricane by the maximum sustained wind speed and the minimum pressure. The relationship between these two quantities is approximately linear. Hurricane A had a maximum sustained wind speed of

Question

150
knots and a minimum pressure of
873

mb
(millibars). Hurricane B had maximum sustained winds of
76
knots and a pressure of
564

mb
.
(c) Hurricane C had a maximum wind speed of
105
knots. Using the equation found in part (b), predict the minimum pressure.
The minimum pressure was approximately

mb
. Round to the nearest whole number.

Answer 1

To find the relationship between maximum sustained wind speed and minimum pressure, we can use the information given about Hurricane A and Hurricane B.

First, let's find the equation for the relationship between maximum sustained wind speed (W) and minimum pressure (P).

For Hurricane A:
W = 150 knots
P = 873 mb

For Hurricane B:
W = 76 knots
P = 564 mb

Using the given information, we can set up a linear equation in the form of y = mx + b, where y represents P and x represents W.

Using the points (150, 873) and (76, 564):

m = (P2 - P1) / (W2 - W1)
m = (564 - 873) / (76 - 150)
m = -309 / -74
m ≈ 4.177

Using the point (150, 873) and the value of m calculated above:

873 = 4.177(150) + b

Simplifying:
b = 873 - 4.177(150)
b = 873 - 626.55
b ≈ 246.45

So, the equation for the relationship between maximum sustained wind speed (W) and minimum pressure (P) is:

P = 4.177W + 246.45

Now, to predict the minimum pressure for Hurricane C, where W = 105 knots:

P = 4.177(105) + 246.45
P ≈ 435.865 + 246.45
P ≈ 682.315

Rounding to the nearest whole number, the minimum pressure for Hurricane C is approximately 682 mb.