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

To find the vertical component of the speed of the plane, you can use the sine function to break down the speed into its vertical and horizontal components. The formula is: \[ \text{Vertical Speed} = \text{Total Speed} \times \sin(\theta) \] Where the total speed is 160 mph and \( \theta = 8^{\circ} \). Plugging in the numbers: \[ \text{Vertical Speed} = 160 \, \text{mph} \times \sin(8^{\circ}) \approx 160 \, \text{mph} \times 0.14 \approx 22.4 \, \text{mph} \] So, the vertical component of the speed of the plane is approximately 22.4 mph. Now, you might think this is just math, but it’s actually essential in aviation! Pilots need to know how much lift they're generating, which is essential for maintaining altitude and safety during takeoff. Calculating the vertical component helps them understand the performance of the aircraft in various situations. If you ever find yourself confused about resolving vector components, remember: visualization can be your best friend! Draw a right triangle with the plane's speed as the hypotenuse and label the vertical and horizontal components. This method can help you avoid common mistakes, like forgetting to use the correct angle or function. Keep practicing with different angles, and soon you'll master resolving any vector!