What are the steps to find the resultant velocity when an airplane encounters a wind?

Question

Bernie · Answer

a. Drawing the Vectors  To find the resultant velocity when an airplane encounters a wind, we need to add the velocity vectors of the airplane (ū) and the wind (w). Begin by drawing a head-to-tail configuration for v and w, representing the airplane's velocity and the wind's velocity.  b. Writing in Component Form  Write both ū and w in component form by breaking down their x and y components. Use the formulas magnitude * cos(angle) for the x-component and magnitude * sin(angle) for the y-component.  c. Finding the Resultant Vector in Component Form  Calculate the resultant vector ū + w in component form by adding the x-components of ū and w together, and the y-components of ū and w together.  d. Converting to Polar Form  Convert the resultant vector ū + w to polar form using the formulas: magnitude = sqrt(x^2 + y^2) and angle = tan^-1(y/x).  e. Analyzing the Result  The answer to part (c) will provide the magnitude and direction of the resultant vector, indicating the speed and heading of the airplane counterclockwise from due east.  Remember to include the values of the magnitudes and angles in your final answer.

Suppose an airplane encounters a wind: finding resultant velocity

a. Drawing the Vectors

b. Writing in Component Form

c. Finding the Resultant Vector in Component Form

d. Converting to Polar Form

e. Analyzing the Result

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