Question

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 472 kw in a 12 m/s wind, how much power does it generate in a 15 m/s wind?

a) 921 kw
b) 944 kw
c) 843 kw
d) 749 kw

Answer 1

The wind turbine generates approximately 944 kW of power in a 15 m/s wind.

Step-by-step explanation:

To solve this problem, we can use the concept of direct variation. The power generated by a wind turbine varies directly as the cube of the wind speed. Let's assume the power generated in a 15 m/s wind is P kW. According to the given information, we have the following proportion:

12^3/472 = 15^3/P

Cross-multiplying, we get:
12^3 * P = 472 * 15^3

Simplifying the equation and solving for P, we find that the wind turbine generates approximately 944 kW of power in a 15 m/s wind. Therefore, the answer is option b) 944 kW.