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).

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

Answer 1

P = kv^3

So,
P/v^3 is constant.

You want P such that

P/12^3 = 500/10^3

Answer 2

It equal P=864kw

Answer 3

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Answer 4

we all here at the ame time wednesday feb,16 2022 :')

Answer 5

Well, if the power generated by a wind turbine varies directly as the cube of the wind speed, we can use that information to solve this problem.

Let's call the power generated in the 12m/s wind P2. According to the given information, we know that:

P1 = 500kW
v1 = 10m/s
v2 = 12m/s

Since power varies directly with the cube of the wind speed, we can set up the following equation:

P1 / v1^3 = P2 / v2^3

Plugging in the given values:

500kW / (10m/s)^3 = P2 / (12m/s)^3

Simplifying:

500kW / 1000m^3/s^3 = P2 / 1728m^3/s^3

Cross-multiplying:

500kW * 1728m^3/s^3 = P2 * 1000m^3/s^3

Simplifying further:

864000kW*m^3/s^3 = P2 * 1000m^3/s^3

Dividing both sides by 1000m^3/s^3:

864kW = P2

So, in a 12m/s wind, the turbine would generate 864kW of power.

And just remember, it's not just the wind that will blow you away with these calculations.

Answer 6

To find out how much power the turbine generates in a 12m/s wind, we need to use the concept of direct variation and the relationship between power and wind speed provided in the problem.

According to the problem, the power generated by the wind turbine varies directly as the cube of the wind speed. This can be represented mathematically as:

P ∝ v^3

where P is the power generated by the turbine and v is the wind speed.

To solve for the constant of variation, we can use the fact that the turbine generates 500kW in a 10m/s wind. We can rewrite the equation as:

P = k * v^3

Substituting the given values, we have:

500 = k * 10^3

To find the value of k, we divide both sides of the equation by 10^3:

k = 500 / (10^3)

k = 0.5

Now that we have the value of k, we can use it to find the power generated by the turbine in a 12m/s wind. We substitute the wind speed into the equation:

P = 0.5 * 12^3

P = 0.5 * 1728

P = 864 kW

Therefore, the turbine generates 864 kW of power in a 12m/s wind.

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).

P = kv^3

It equal P=864kw

thank you

bro you already know cuh we pushin 🅿 ong

we all here at the ame time wednesday feb,16 2022 :')

Well, if the power generated by a wind turbine varies directly as the cube of the wind speed, we can use that information to solve this problem.

To find out how much power the turbine generates in a 12m/s wind, we need to use the concept of direct variation and the relationship between power and wind speed provided in the problem.