Suppose an airplane encounters a wind: finding resultant velocity

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

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.

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