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 42 m/s. The plane is in a 18 m/s wind blowing toward the southwest relative to earth.

Please show equations used and why. Thank you.

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 42 m/s. The plane is in a 18 m/s wind blowing toward the southwest relative to earth. letting x be east and y be north, find the components of (the velocity of the plane relative to the earth. Find the magnitude of Find the direction of

Explanation / Answer

vP/W = -42*j. (i denote x-axis and j denote y-axis)
vW/E= -18*sin45*i-18*cos45*j=-12.7*i-12.7*j.
we have
vP/E=vP/W+vW/E=-54.7*j-12.7*i.
so vx=-12.7 and vy=-54.7
b. magnitude v=sqrt(12.7^2+54.7^2)=56.15(m/s).
c. direction (with x-axis counter clockwise be positive).
tan alpha = -54.7 / -12.7
so alpha = 256.92(deg)

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