3. An airplane has an airspeed of 150 m/s with 40 m/s head wind (as measured fro

Question

3. An airplane has an airspeed of 150 m/s with 40 m/s head wind (as measured
from the ground) at an angle of 20° with the major axis of the airplane. Theairplane is not compensate for any lateral drift.
(i) Calculate the two components of the velocity of the airplane (along its axis andperpendicular to its axis) as measured from the ground. 112 m/s and 14 m/s (anysign is fine)
(ii) Calculate the speed of teh airplane as measured from the ground. 113 m/s

The answers are in bold, but I do not understand how to calculate them. Could you please draw it out and explain?

Explanation / Answer

assume plane is going in horizontal direction ( + x direction )

wind coming at angle of 20 degree

wind has two component in + x direction

+y direction

if both in same direction the observer will see the velocity of plane = 150 - 40cos20 = 112.4 = 112 m/s

in y direction there is only one component = 40 sin20 = 13.68 = 14 m/s

part 2 )

|v| = sqrt(vx^2+vy^2)

|v| = 113.2 m/s = 113 m/s

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