Question 816597
use vector addition:
a = magnitude 150 kph direction to 70 degrees
w = magnitude 25 kph direction to 340 degrees
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convert angles from true north (aviation format), to polar coordinates:
70 degrees true north = +20 degrees polar
340 degrees true north = +110 degrees polar
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calculate the rectangular coordinates of each vector:
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a vector:
ay:
sin( 20 ) = opp/hyp
sin( 20 ) = ay/150
ay = 150 * sin( 20 )
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ay = 51.303
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ax:
cos( 20 ) = adj/hyp
cos( 20 ) = ax/150
ax = 150 * cos( 20 )
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ax = 140.953
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w vector:
wy:
sin( 110 ) = opp/hyp
sin( 110 ) = wy/25
wy = 25 * sin( 110 )
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wy = 23.492
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wx:
cos( 110 ) = adj/hyp
cos( 110 ) = wx/25
wx = 25 * cos( 110 )
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wx = -8.551
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calculate the result vector, from vector addition in rectangular coordinates
r vector:
rx:
rx = ax + wx
rx = 140.953 - 8.551
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rx = 132.402
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ry:
ry = ay + wy
ry = 51.303 + 23.492
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ry = 74.795
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convert r vector to polar coordinates:
rmag = sqrt( 132.402^2 + 74.795^2 )
rmag = 152.067 kph
rang = arctan( 74.795 / 132.402 )
rang = 29.462 degrees
convert polar angle to aviation format (true north)
rang = 60.538 degrees
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Answer:
the airplane's actual heading after wind correction is 60.538 degrees, and its ground speed accounting for wind is 152.067 kph
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