I need clear solutions(step by step) to each step. Please make sure it\'s legibl

Question

I need clear solutions(step by step) to each step. Please make sure it's legible

If an airplane travels towards the south at 35 metros/seg. And there is wind of 10 metros/seg. that blows towards the southwest at 35 degree (As shown in the following image): a) What is the vector of speed of the airplane relative to the earth? b) Determine the magnitude of the vector and the speed of the airplane relative to the earth? c) What is the angle of the vector of speed of the airplane relative to the earth?

Explanation / Answer

vector speed of airplane relative to air Vpa = -35 j

vector speed of air relative to earth VaE = -10*sin35 i - 10*cos35 j

vector speed of airplane relative to earth VpE = Vpa + VaE

VpE = -35 j - 10*sin35 i - 10*cos35 j

VpE = -5.74 i - 43.2 j

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(b)

magnitude = sqrt(5.74^2+43.2^2) = 43.6 m/s

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(c)

angle = tan^-1(43.2/5.74) = 82.43   southwest

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