Discussion
The aircraft velocity (m/s) components in body axes are given as [u, v, w] = [100, 10, 10]. The air velocity (m/s), angle of attack (deg) and sideslip angle (deg) in that order are
Answer: D
The air velocity, angle of attack and sideslip angle are [100.995, 5.71, 5.68].
\[ \begin{aligned} V &= \sqrt{100^{2} + 10^{2} + 10^{2}} = \sqrt{10200} \\ &\approx 100.995\ \text{m/s} \\ \alpha &= \tan^{-1}(w/u) = \tan^{-1}(0.1) \approx 5.71^\circ \\ \beta &= \sin^{-1}(v/V) = \sin^{-1}(0.0990) \approx 5.68^\circ \end{aligned} \]
The angles differ slightly because the angle of attack uses the tangent in the x-z plane while the sideslip uses the sine against the full speed. The entries 0.1 are the ratio \(w/u\) left unconverted, and 5.73 is 0.1 radian expressed in degrees; 120 and 100 are not the magnitude of the velocity vector.
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