Please explain how to do this problem, Ive been working on it forever! This is t

Question

Please explain how to do this problem, Ive been working on it forever! This is the entire problem, it should be able to be solved with the information given.

An airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction 27° south of east. Its direction of motion relative to the earth is 45.0° south of west, while its direction of travel relative to the air is 9° south of west.

(a) What is the airplane's speed relative to the air mass in meters per second?

(b) What is the planes speed relative to the earth in m/s?

Explanation / Answer

(a)

velocity of steam , vs = 45.0 * (cos(27) i - j * sin(27)) m/s

vs = 40.1 i - 20.4 j m/s

Now, speed of plane relative to air

vpa = vpa *(- cos(45) i - sin(45) j )

Now, velocity of plane relative to ground

Vp = Vp * (- cos(9) i - j * sin(9))

Now, for the plane

Vpa = Vp + Vs

vpa *(- cos(45) i - sin(45) j ) = 40.1i - 20.4 j + Vp * (- cos(9) i - j * sin(9))

which gives

-cos(45) * vpa = 40.1 - vp * cos(9) ---------(1)

-sin(45) * vpa = -20.4 - vp * sin(9) ---------(2)

solving 1 and 2

vpa = 34.08 m/s

vp = 23.70 m/s

the airplane's speed relative to air is 34.08 m/s

b)

airplane's speed relative to earth is 23.70 m/s

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