A model 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.

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Muscardinus Muscardinus · Answer 1 · 2019-09-25T06:37:14+02:00

Explanation:

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

Velocity due north, [tex]v_a=44j\ mi/hr[/tex]

Velocity of the crosswind, [tex]v_w=44i\ mi/hr[/tex]

Velocity of downdraft, [tex]v_d=-22k\ mi/hr[/tex] (downward direction)

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

[tex]v=44i+44j-22k[/tex]

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

[tex]v=\sqrt{44^2+44^2+22^2}[/tex]

v = 66 m/s

Hence, this is the required solution.