A commercial aircraft plans to fly along the straight route represented by the vector
d=800i+600j+1200k
(all components in kilometres relative to a fixed origin). A steady wind gives the aircraft an additional velocity
w=50i−30j+20kkmh−1.
Answer the following questions concerning the effect of the wind.
(i) Find the component of the wind velocity along the intended route d.
(ii) Determine the component of the wind velocity perpendicular to d.
(iii) Hence calculate the effective speed of the aircraft in the intended direction and the magnitude of the drift velocity produced by the wind.
(iv) Interpret the signs of the results obtained in parts (i) and (ii), stating whether the wind assists or opposes the aircraft’s progress and whether it causes sideways drift.