Question

Wind farms are a source of renewable energy found around the world. The power P generated by a wind turbine varies directly as the cube of the wind speed v If a turbine generates 500KW in a 10m/s wind, how much power does it generate in a 12m/s wind?

A. 57122KW
B. 4394KW
C. 11424KW
D. 22849KW​

Answer 1

The wind turbine generates approximately 228.49KW of power in a 12m/s wind.

Step-by-step explanation:

The power generated by a wind turbine varies directly as the cube of the wind speed. In this case, the turbine generates 500KW of power in a 10m/s wind. To find out how much power it generates in a 12m/s wind, we can set up a proportion:

P1/v1^3 = P2/v2^3

Substituting the given values:

500/10^3 = P2/12^3

Simplifying the proportion gives:

500/1000 = P2/1728

Finally, solving for P2, we find that the turbine generates approximately 228.49KW of power in a 12m/s wind.