An airplane pilot sets a compass course due west and maintains an airspeed of 21

Question

An airplane pilot sets a compass course due west and maintains an airspeed of 210km/h . After flying for a time of 0.520h , she finds herself over a town a distance 121km west and a distance 20km south of her starting point.

A. Find the magnitude of the wind velocity.

B. Find the direction of the wind velocity.

C. If the wind velocity is 41km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 210km/h . (Express your answer as an angle measured north of west)

Explanation / Answer

her resultant speed due west = 121/0.52 = 232.69 kmph.
so airspeed due west is 232-210 = 22 kmph.
airspeed due south is 20/0.52 = 38.46 kmph.
the magnitude of the wind velocity = sqrt ( 22^2 + 38.46^2 ) = 44.31 kmph.
the angle of airspeed south of west is arctan ( 38.46/22) = 60.23 degrees.
if wind velocity is 41 kmph due south, her velocity should have 41 kmph component in north dir.
so component west = sqrt ( 210^2 - 41^2 ) = 205.96 kmph.
the angle north of west is arctan( 41/205.96 ) = 11.26 degrees.

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