A wind turbine generates 1200 kW of power in a 20 mi/h wind.
How much power does this turbine generate in a 12 mi/h wind?
Use the formula for P as a power function of velocity, P=av^3
To find the power generated by the wind turbine in a 12 mi/h wind, we can use the formula P=av^3, where P is the power and v is the wind velocity.
Let's first find the constant of proportionality, a, using the given information.
In a 20 mi/h wind, the wind turbine generates 1200 kW of power.
So, we can write the equation as:
1200 = a(20)^3
Simplifying, we have:
1200 = a(8000)
a = 1200/8000
a = 0.15
Now, let's use this value of a to find the power generated in a 12 mi/h wind:
P = 0.15(12)^3
P = 0.15(1728)
P = 259.2 kW
Therefore, the wind turbine generates 259.2 kW of power in a 12 mi/h wind.