Resultant direction of aircraft

[gkraju]

in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ?

 

[Filip Larsen]

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[NatSusan]

Based on the information provided, we can calculate the direction and magnitude of the aircraft's velocity vector as follows:

1. Calculate the magnitude of the wind velocity vector:
Magnitude of wind velocity vector = √(2^2 + 7^2 + 20^2) = √453 = 21.27 knots

2. Calculate the direction of the wind velocity vector:
Direction of wind velocity vector = arctan(20/√(2^2 + 7^2)) = 71.56 degrees

3. Calculate the magnitude of the aircraft's velocity vector:
Magnitude of aircraft's velocity vector = √(4^2 + 7^2 + 3^2) = √74 = 8.60 knots

4. Calculate the direction of the aircraft's velocity vector:
Direction of aircraft's velocity vector = arctan(3/√(4^2 + 7^2)) = 21.80 degrees

Therefore, the direction of the aircraft's velocity vector is 21.80 degrees and its magnitude is 8.60 knots.