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Chapter 2: 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, the destructive power of the hurricane quadruples.

Step by step solution

01

Understand the Relationship

Firstly, understand that the problem states the wind pressure \(P\) is directly proportional to the square of the wind velocity \(V\). This can be represented as \(P = kV^2\) where \(k\) is a constant of proportionality.
02

Double the Velocity

Then, consider what happens when the wind speed, or velocity, doubles. If the original velocity is \(V\), then the new velocity is \(2V\). Now, substitute this back into the equation: \(P' = k(2V)^2\). Simplify this equation to \(P' = 4kV^2\).
03

Compare the Initial and Final Pressure

Now, compare the new pressure \(P'\) with the original pressure \(P\). You can see that \(P'\) is four times larger than \(P\), which means the destructive power of the hurricane, as measured by wind pressure, will quadruple when the wind speed doubles.

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