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 700kW in a 5 m/s wind, how much power does it generate in a 14 m/s wind?
A. 76,832 kw
B. 5,488 kW
C. 15,366 kW
D. 30,733 kW

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 700kW in a 5 m/s wind, how much power does it generate in a 14 m/s wind?
A. 76,832 kw 
B. 5,488 kW
C. 15,366 kW
D. 30,733 kW

anonymous · Answer

$$P = a \times  v^3$$
Input given values:
$$700kW = a \times 5^3$$
Solve for a:
$$a = 5.6000$$

Now use:
$$P = a \times  v^3$$
$$P = 5.6000 \times  14^3$$
$$P = 15366.4$$
$$15366.4kW$$