A model airplane is flying horizontally due south at 12 mi/hr when it encounters a horizontal crosswind blowing west at 12 mi/hr and a downdraft blowing vertically downward at 6 mi/hr. a. Find the position vector that represents the velocity of the plane relative to the ground. b. Find the speed of the plane relative to the ground. a. Let the unit vectors i, j, and k point east, north, and upward, respectively. Begin by writing vectors describing the velocity of the plane relative to the air, the crosswind, and the downdraft. Find the vectors representing the velocity of the plane relative to the air va, the velocity of the horizontal crosswind vw, and the velocity of the vertical downdraft va- Va = (Di+ Dj+ (Ok Vw = (| Di+ I Di+ Dk Va = Di+ ODi+ (Dk The position vector of the velocity relative to the ground is (Di+ (Dj+ Ok b. The speed of the plane relative to the ground is

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