Question

the mean sustained wind velocity, v, can be determined by the equation $v = 6.3\sqrt{1013 - p}$, where p 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?
910 millibars
363 millibars
103 millibars
194 millibars

Explanation:

Step1: Substitute \( v = 64 \) into the equation

We have the equation \( v = 6.3\sqrt{1013 - p} \). Substitute \( v = 64 \) into it: \( 64 = 6.3\sqrt{1013 - p} \).

Step2: Solve for \( \sqrt{1013 - p} \)

Divide both sides by \( 6.3 \): \( \sqrt{1013 - p}=\frac{64}{6.3}\approx10.16 \).

Step3: Square both sides

Square both sides of the equation \( \sqrt{1013 - p}\approx10.16 \) to get \( 1013 - p\approx(10.16)^2\approx103.2 \).

Step4: Solve for \( p \)

Rearrange the equation to solve for \( p \): \( p\approx1013 - 103.2\approx909.8\approx910 \).

Answer:

910 millibars