Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). If a turbine generates 500 kW in a 10 ms/

Question

wind, how much power does it generate in a 12 ms/
wind?

(2 points)

Answer 1

To solve this problem, we can set up a proportion using the formula for direct variation.

We know that the power P generated by a wind turbine varies directly as the cube of the wind speed v. So, we can write the proportion as:

P/500 = (v/10)^3

To find the power generated in a 12 m/s wind, we can substitute the value of wind speed (v) into the proportion and solve for P.

P/500 = (12/10)^3
P/500 = (1.2)^3
P/500 = 1.728

Cross multiplying gives us:

P = 1.728 * 500
P = 864

Therefore, the turbine generates 864 kW in a 12 m/s wind speed.