posted by Shayne on .
A pilot wishes to fly 450 km due south in 3 hours. A wind is blowing from the west at 50 km/hr. By means of a vector diagram, compute the proper heading and speed that the pilot must choose to achieve this objective.
From the origin,draw a vector on the positive x axis pointing eastward.Label
it 50 km/h.
Draw a vector on the negative y axis pointing south. Label it -150 km/h.
From the origin, draw the resultant vector between the two original vectors
and pointing southeast.
tanA = Y/X = -150/50 = -3,
A = -71.6 deg. = 288.4 deg. CCW.
R = X / cosA = 50 / cos288.4 = 158.4km / h .
288.4 - 270 = 18.4 deg East of the
To allow for windage, the plane must head 18.4 deg west of due South:
270 - 18.4 = 25i.6 deg.CCW.
d = 3 h * 158.4 km/h = 475.2 km.