\begin{tabular}{l} If a 737 takes off at an \( 8^{\circ} \) angle going 160 mph , \\ what is the horizontal component of the speed of \\ the plane? (Note: \( \sin \left(8^{\circ}\right) \approx 0.14, \cos \left(8^{\circ}\right) \approx 0.99 \), \\ \( \left.\tan \left(8^{\circ}\right) \approx 0.14\right) \) \\ \hline\end{tabular}

To find the horizontal component of the speed of the plane, we can use the cosine function. The horizontal speed (Vx) can be calculated using the formula: \[ Vx = V \cdot \cos(\theta) \] where \( V = 160 \) mph and \( \theta = 8^{\circ} \). Substituting the values in, we have: \[ Vx = 160 \cdot \cos(8^{\circ}) \approx 160 \cdot 0.99 \approx 158.4 \text{ mph} \] So, the horizontal component of the speed of the 737 is approximately 158.4 mph. Now let's consider real-world applications of these calculations. Pilots use trigonometric functions like sine and cosine frequently to determine flight paths, ensuring that they can take off and land safely with calculated angles and speeds. This knowledge is crucial not just for flying but also for landing maneuvers where maintaining an accurate horizontal speed relative to the runway is essential. Another engaging aspect of flight dynamics is the importance of avoiding common mistakes. A frequent error in such calculations is using the wrong trigonometric function or misinterpreting the angle's relation to horizontal and vertical components. Remember, sine relates to the vertical component (height), while cosine deals with the horizontal component, so keep that in mind to avoid a bumpy math ride!