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 500 kW in a 10 ms/ wind, how much power does it generate in a 12 m/s wind?
To solve this problem, we can use the direct variation formula:
P1/v1^3 = P2/v2^3
where P1 is the initial power (500 kW), v1 is the initial wind speed (10 m/s), P2 is the unknown power we want to find, and v2 is the new wind speed (12 m/s).
Plugging in the values we know:
500/10^3 = P2/12^3
Simplify to find P2:
500/1000 = P2/1728
0.5 = P2/1728
Multiply both sides by 1728 to solve for P2:
P2 = 0.5 * 1728
P2 = 864 kW
Therefore, the turbine would generate 864 kW in a 12 m/s wind speed.