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Chapter 3: Problem 53

In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind pressure is a measure of a hurricane's destructive capacity, what happens to this destructive power when the wind speed doubles?

Short Answer

Expert verified
When the wind speed doubles in a hurricane, its destructive power (wind pressure) increases by four times.

Step by step solution

01

Understand the relationship between wind pressure and wind velocity

From the problem statement, we know that wind pressure \( P \) is directly proportional to the square of the wind velocity \( V^2 \). Mathematically, we express this as \( P = kV^2 \), where \( k \) is the constant of variation.
02

Identify what the question asks

The question asks what happens to the destructive power when the wind speed doubles. This means if the initial wind speed is\( V \), we are required to find the new pressure \( P' \) when the wind speed is \( 2V \).
03

Apply the relationship to doubling the wind velocity

We substitute \( V \) with \( 2V \) in our equation. Therefore, the new pressure \( P' \) when the wind speed is \( 2V \) would be \( P' = k(2V)^2 =4kV^2 \).
04

Compare the new pressure with the old pressure

By comparing the new pressure \( P' = 4kV^2 \) with the old pressure \( P = kV^2 \), we can see that the new pressure is four times the old pressure. This means that the destructive power, when the wind speed doubles, is four times higher.

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