The nose of an ultralight plane is pointed south, and its airspeed indicator sho

Question

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 44 m/s. The plane is in a 12 m/s wind blowing toward the southwest relative to the earth.

1.) Letting x be east and y be north, find the components of Vp/E (the velocity of the plane relative to the earth).

Express your answers using two significant  figures, separated by commas.

Vx, Vy =  ?  m/s

2.) Find the magnitude of Vp/E.

Vp/E =  ?  m/s

3.) Find the direction of Vp/E.

I have no idea how to do this problems! Please show step by step so I can try to understand.

THANK YOU!!!

Explanation / Answer

(a) Velocity relative to earth is the sum of
-40 m/s y + 17 m/s (- x/sqrt(2) - y/sqrt(2)),
where x and y are unit vectors in the east and north directions.
v = - 12.02 m/s x + -52.02 m/s y

(b) sqrt(12.02^2 + 52.02^2) = 53.4 m/s

(c) arctan (52.02/12.02) = 77.0 degrees south of west

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