Answered

The mean sustained wind velocity, [tex]\( v \)[/tex], can be determined by the equation [tex]\( v=6.3 \sqrt{1013-p} \)[/tex], where [tex]\( p \)[/tex] is the air pressure, in millibars, at the center of the hurricane.

What is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second?

A. 103 millibars
B. 194 millibars
C. 363 millibars
D. 910 millibars



Answer :

GinnyAnswer
To determine the approximate air pressure at the center of a hurricane given that the mean sustained wind velocity is 64 meters per second, we need to use the given equation:

[tex]\[ v = 6.3 \sqrt{1013 - p} \][/tex]

Given:
[tex]\[ v = 64 \, \text{meters per second} \][/tex]

We will isolate [tex]\( p \)[/tex] in the equation to find the air pressure. Here's the step-by-step solution:

1. Start with the given equation:
[tex]\[ v = 6.3 \sqrt{1013 - p} \][/tex]

2. Substitute the given wind velocity [tex]\( v = 64 \)[/tex]:
[tex]\[ 64 = 6.3 \sqrt{1013 - p} \][/tex]

3. Divide both sides by 6.3 to isolate the square root term:
[tex]\[ \frac{64}{6.3} = \sqrt{1013 - p} \][/tex]

4. Calculate the left side:
[tex]\[ \frac{64}{6.3} \approx 10.1587 \][/tex]

5. Square both sides to remove the square root:
[tex]\[ (10.1587)^2 = 1013 - p \][/tex]

6. Perform the squaring operation:
[tex]\[ 103.196 = 1013 - p \][/tex]

7. Rearrange to solve for [tex]\( p \)[/tex]:
[tex]\[ p = 1013 - 103.196 \][/tex]

8. Subtract to find [tex]\( p \)[/tex]:
[tex]\[ p \approx 909.804 \][/tex]

Therefore, the approximate air pressure at the center of the hurricane is [tex]\( 910 \)[/tex] millibars when rounded to the nearest whole number. Among the given choices, the closest answer is:

[tex]\[ \boxed{910 \text{ millibars}} \][/tex]