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
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.
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.
To find the minimum pressure for Hurricane C, we need to use the equation that relates the maximum sustained wind speed and the minimum pressure.
From the given information, we know that Hurricane A had a maximum sustained wind speed of 150 knots and a minimum pressure of 873 mb, as well as Hurricane B had a maximum sustained wind speed of 76 knots and a minimum pressure of 564 mb.
We can use this information to find the equation for the relationship between wind speed and pressure. Let's assume that the relationship is linear:
slope = (pressureB - pressureA) / (windSpeedB - windSpeedA)
= (564 mb - 873 mb) / (76 knots - 150 knots)
= -309 mb / (-74 knots)
= 4.1757 mb/knot
Using the slope, we can then find the equation for the relationship between wind speed and pressure:
pressureC = slope * windSpeedC + intercept
Now, we need to find the intercept using one of the data points. Let's use Hurricane A:
pressureA = slope * windSpeedA + intercept
intercept = pressureA - slope * windSpeedA
= 873 mb - 4.1757 mb/knot * 150 knots
= 873 mb - 626.36 mb
= 246.64 mb
Now we can substitute the values into the equation to find the pressure for Hurricane C:
pressureC = slope * windSpeedC + intercept
= 4.1757 mb/knot * 105 knots + 246.64 mb
= 437.8485 mb + 246.64 mb
= 684.4885 mb
Rounding to the nearest whole number, the minimum pressure for Hurricane C is approximately 684 mb.
To find the minimum pressure of Hurricane C given its maximum wind speed, we need to use the relationship between maximum sustained wind speed and minimum pressure that was determined in part (b).
We are given the maximum wind speed of Hurricane C as 105 knots. As per the problem statement, we assume that the relationship between wind speed (V) and pressure (P) is linear.
From part (b), we know that the equation relating wind speed (V) and pressure (P) can be expressed as:
P = mV + b
Using the information from Hurricanes A and B, we can determine the values of m and b.
For Hurricane A:
wind speed (V_A) = 150 knots
pressure (P_A) = 873 mb
For Hurricane B:
wind speed (V_B) = 76 knots
pressure (P_B) = 564 mb
To find the values of m and b, we can use the slope-intercept form of a linear equation:
m = (P_B - P_A) / (V_B - V_A)
b = P_A - mV_A
Plugging in the values:
m = (564 mb - 873 mb) / (76 knots - 150 knots)
m = -309 mb / -74 knots
m ≈ 4.18 mb/knots
b = 873 mb - (4.18 mb/knots)(150 knots)
b ≈ 873 mb - 627 mb
b ≈ 246 mb
Now that we have determined the values of m and b, we can use them to predict the minimum pressure for Hurricane C given its maximum wind speed of 105 knots.
P_C = mV_C + b
P_C = (4.18 mb/knots)(105 knots) + 246 mb
P_C ≈ 439 mb + 246 mb
P_C ≈ 685 mb
Therefore, the minimum pressure for Hurricane C is approximately 685 mb. Rounding it to the nearest whole number, we get 685 mb.