Amodel airplane is flying horizontally due north at 44 mi/hr when it encounters a horizontal crosswind blowing east at 44 mi/hr and a downdraft blowing vertically downward at 22 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.

Explanation:

Let i, j and k represents east, north and upward direction respectively.

Velocity due north,

Velocity of the crosswind,

Velocity of downdraft, (downward direction)

(a) Let v is the position vector that represents the velocity of the plane relative to the ground. It is given by :

(b) The speed of the plane relative to the ground can be calculated as :

v = 66 m/s

Hence, this is the required solution.

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