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 in v (in meters per second). If a turbine generates 500kW in a 10m/s wind, how much power does it generate in 12m/s wind?

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Mathematics

House

20 November, 10:35

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 in v (in meters per second). If a turbine generates 500kW in a 10m/s wind, how much power does it generate in 12m/s wind?

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Danica · Answer 1

If a turbine generates 500kW in a 10m/s wind, how much power does it generate in 12m/s wind?

first solve the proportionality constant k

P = kv^3

500 = k (10^3) k = 500 / 10^3k = 0.5

so when v = 12 m/s

P = 0.5 (12^3) p = 864 kW is the power generated by a 12 m/s wind