Calculate the wind velocity for the situation shown in Figure 3.44. The plane is known to be

Question:

Calculate the wind velocity for the situation shown in Figure 3.44. The plane is known to be moving at 45.0 m/s due north relative to the air mass, while its velocity relative to the ground (its total velocity) is 38.0 m/s in a direction 20.0° west of north.Vtot = 38.0 m/s y (north) x (east) 0 V. W Vtot 70 5 Vp = 45.0 m/s -20.0 110

Strategy

In this problem, somewhat different from the previous example, we know the total velocity Vtot and that it is the sum of two other velocities, Vw (the wind) and Vp (the plane relative to the air mass). The quantity Vp is known, and we are asked to find Vw. None of the velocities are perpendicular, but it is possible to find their components along a common set of perpendicular axes. If we can find the components of Vw, then we can combine them to solve for its magnitude and direction. As shown in Figure 3.44, we choose a coordinate system with its x-axis due east and its y-axis due north (parallel to vp). (You may wish to look back at the discussion of the addition of vectors using perpendicular components in Vector Addition and Subtraction: Analytical Methods.)

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