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(a) An airplane is flying in a jet stream that is blowing at 45.0 m/s in...

(a) An airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction 28° south of east. Its direction of motion relative to the earth is 45° south of west, while its direction of travel relative to the air is 6° south of west. What is the airplane's speed relative to the air mass? (m/s) (b) What is the airplane's speed relative to the earth? (m/s)

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Answer #1

I convert to "standard" angles first (measured ccw from +x axis)
28º south of east = -28º = 332º
45º south of west = 225º
6º south of west = 186º

Vplane w/r/t ground = Vplane w/r/t air + Vair w/r/t ground

x-components:
Vp/g*cos225 = Vp/a*cos186 + 45.0cos332
-0.7071*Vp/g = -0.9945*Vp/a + 39.732
Vp/g = 1.4064*Vp/a - 56.19

y-components:
Vp/g*sin225 = Vp/a*sin186 + 45.0sin332 → substitute for Vp/g
(1.4064*Vp/a - 56.19)*-0.7071 = -0.1045*Vp/a - 21.126
which solves to
Vp/a = 68.382 m/s

VP/g =39.983 m/s

I hope it was helpful.. please rate me positive

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