Question

1. wind turbines convert wind energy into a useful energy like electricity. the formula for wind power is shown below.

( p = 0.5dev^a^3 )

( d ) stands for density, ( e ) for energy efficiency, ( v ) for wind velocity and ( a ) for windmill area. which option shows this formula correctly rearranged to solve for wind velocity, ( v )?

( \bigcirc v = \frac{dea^3}{2p} )

( \bigcirc v = \frac{2p}{dea^3} )

( \bigcirc v = \frac{p}{2dea^3} )

( \bigcirc v = \frac{2dea^3}{p} )

Explanation:

Step1: Start with the given formula

We have the formula for wind power: \( P = 0.5DE V A^{3} \) (assuming the original formula might have a typo and it's \( P = 0.5DE V A^{3} \) where \( V \) is velocity, we need to solve for \( V \)). First, we can rewrite \( 0.5 \) as \( \frac{1}{2} \), so the formula becomes \( P=\frac{1}{2}DE V A^{3} \).

Step2: Isolate the term with \( V \)

To solve for \( V \), we first multiply both sides of the equation by \( 2 \) to get rid of the fraction. So, \( 2P=DE V A^{3} \).

Step3: Solve for \( V \)

Now, we divide both sides of the equation \( 2P = DE V A^{3} \) by \( DE A^{3} \) to isolate \( V \). This gives us \( V=\frac{2P}{DE A^{3}} \).

Answer:

\( V = \frac{2P}{DEA^{3}} \) (corresponding to the option \( V=\frac{2P}{DEA^{3}} \))