A jet airplane flying from Townsville. Australia, has an air speed of 264 m/s in

Question

A jet airplane flying from Townsville. Australia, has an air speed of 264 m/s in a direction 5.0degree south of west. It is in the jet stream, which is blowing at 37 m/s in a direction 15 degree south of east. In this problem you are going to be asked about the velocity of the airplane relative to the Earth. What is the magnitude of the velocity of the airplane relative to the Earth in m/s? What is the angle of the velocity of the airplane relative to the Earth in degrees? Give the angle S of W.

Explanation / Answer

a)
let East be +x axis.

velocity of plain with respect to air,
|v(P/A)| = 264 m/s

in vector notation,
v(P/A) = -264*cos(5) i - 264*sin(5) j

= (-263 i - 23 j) m/s

velocity of air with repcet to ground,

|v(A/G)| = 37 m/s

v(A/G) = 37*cos(15) i - 37*sin(15) j

= (35.7 i - 9.58 j ) m/s

velocity of plain with respect to ground,

v(P/G) = v(P/A) + v(A/G)

= (-263 i - 23 j) + (35.7 i - 9.58 j )

= -227.3 i - 32.6 j ) m/s

|v(P/G)| = sqrt(227.3^2 + 32.6^2)

= 230 m/s <<<<<<<<<-------------------------------Answer

b)
direction : beta = tan^-1(32.6/233)

= 7.96 South of West <<<<<<<<<-------------------------------Answer

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