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 700 kW in a 5 m/s wind, how much power does it generate in a 14 m/s wind? 76,832 kW
5,488 kW
15,366 kW
30,733 kW

Answer 1

\[P=kv ^{3}\]
where k is a constant of proportionality.
We need to find k. Using the data given:
\[k=\frac{P}{v ^{3}}=\frac{700}{5^{3}}\]
In a 14 m/s wind the power generated will be:
\[P=\frac{700}{5^{3}}\times 14^{3}=You\ can\ calculate\]

Answer 2

Alternately, you can use an estimation strategy. If the wind is 10 m/s (twice as much), there will be eight times the power. That would be about 5600 kw. If the wind is fifteen m/s (three times what we started with), the power is 27 times what we started with, or 18900 kW. Since fourteen is a little less, look for an answer a little less than 19000 kW.