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{latex}

$$v=-2.22\ \mathrm{rad/s}\ \mathbf{\hat{k}} \times -44.2\ \mathrm{m}\ \mathbf{\hat{i}}$$
$$v=98.1\ \mathrm{m/s}\ \mathbf{\hat{j}}$$

{latex}

Using Additionally, by using the simple one-dimensional momentum theory, we can estimate the power coefficient which is the fraction of harnessed power to total power in the wind for the given turbine swept area. This analysis uses the following assumptions: 

• The flow is steady, homogenous and incompressible.
• There is no frictional drag.
• There is an infinite number of blades.
• There is uniform thrust over the disc or rotor area.
• The wake is non-rotating.
• The static pressure far upstream and downstream of the rotor is equal to the undisturbed ambient pressure. 

According to the M.Eng report presented in the problem statement, this blade is meant to ressemble GE 1.5 XLE wind turbine blade. The specification sheet of this turbine states the rated power of this turbine to be 1.5 MW, the rated wind speed to be 11.5 m/s and the rotor diameter to be 82.5 m. 

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