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Answer :
Final answer:
To find the actual velocity of the Quinjet affected by a southwest wind, vector addition is used to combine the plane's velocity with the wind's velocity components. The magnitude of the resultant velocity is calculated with the Pythagorean theorem, and its direction is found using trigonometry.
Explanation:
The student is asking about the actual velocity of the Quinjet when it is affected by wind while flying due North at 785 mph and encountering a southwest wind at 98.2 mph. To solve this, we need to use vector addition. The Quinjet's velocity is represented by a vector pointing straight up (north) on our coordinate system, while the wind's velocity vector points southwest (225° from east).
First, we convert the wind's velocity into its northward and eastward components. The northward component (Vn_wind) is 98.2 mph × cos(225°) and the eastward component (Ve_wind) is 98.2 mph × sin(225°). Then, we can combine the Quinjet's velocity with the wind's velocity components to find the resultant velocity vector. The northward component (Vn_resultant) is equal to the Quinjet's velocity plus Vn_wind, while the eastward component (Ve_resultant) is simply Ve_wind since there is no eastward movement by the Quinjet.
After finding the components, we can use the Pythagorean theorem to calculate the magnitude of the resultant velocity and trigonometry to find its direction. The actual velocity and direction will provide the Quinjet's course correction necessary to maintain a due North trajectory against the wind.
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