Final answer:
When wind speeds go from 10 m/s to 12 m/s, the power generated by the wind turbine is expected to increase to 864 kW due to the cubic relationship between power output and wind speed. None of the provided answer choices match this calculated value.
Step-by-step explanation:
The amount of power generated by a wind turbine is proportional to the cube of the wind speed. When the wind speed increases, the power output increases significantly. Given that a turbine generates 500 kW at a 10 m/s wind speed, we can use the cube of the ratio of the two wind speeds to calculate the power output at the new speed:
Power at new speed = Power at 10 m/s × (New speed / Original speed)^3
Power at 12 m/s = 500 kW × (12 m/s / 10 m/s)^3
Power at 12 m/s = 500 kW × (1.2)^3
Power at 12 m/s = 500 kW × 1.728
Power at 12 m/s = 864 kW (rounded to two decimal places)
Since none of the answer choices matches this calculated value, the question may have an error or may be missing the correct answer choice. The options given do not reflect the correct power output based on the cube relationship between power and wind speed.