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?

Question

agent0smith · Answer

So power, P in kW is directly proportional to the cube of the wind speed, w in m/s. 
$$P = kw ^{3}$$ 
k is a constant of proportionality, which we can find by entering P = 700 kW and w = 5 m/s.

agent0smith · Answer

$$700 = k \times 5^{3}$$
Solve that for k, and then we want to know P when w = 14 m/s:
$$P = k \times 14^{3}$$

anonymous · Answer

how do i solve it though?

agent0smith · Answer

for k, we had
$$700 = k \times 5^{3}$$
so we need to rearrange to find k. so divide both sides by 5^3 (5^3 = 125):
$$k = \frac{ 700 }{ 5^3} = \frac{ 700 }{ 125 }$$

anonymous · Answer

ohh ok thanks.. so would it be 5,488

agent0smith · Answer

Wait, how'd you get 5488?

agent0smith · Answer

k = 700/125 = 5.6. Now we have the formula for P:

$$P = 5.6 w ^{3}$$
And we can find the power, P, when the wind speed, w = 14m/s.

agent0smith · Answer

Don't forget the units for P, kW.

$$P = 5.6 \times 14^{3} kW$$