Answer:
7 m/s
Explanation:
We know that the electrical power produced and the speed of the wind are related by:
[tex]P(v)=1.167v^3[/tex]
Then, if the electrical power produced is 400 kW, we can write the following equation:
[tex]400=1.167v^3[/tex]
So, we need to solve the equation for v to know the speed of the wind.
[tex]\begin{gathered} 1.167v^3=400 \\ \frac{1.167v^3}{1.167}=\frac{400}{1.167} \\ v^3=342.76 \\ v=\sqrt[3]{342.76}=6.99\approx7 \end{gathered}[/tex]
Therefore, the speed of the wind is approximately 7 m/s