An aircraft leaves an airport and flies 250\,km at an angle of 30∘ north of east. It then turns and flies 320\,km due east before reaching its destination.
(a) Express each leg of the flight in terms of its x- and y-components, taking east as the +x-direction and north as the +y-direction.
(b) Obtain the total displacement vector of the aircraft from the airport to the destination in component form.
(c) Calculate the magnitude of this displacement.
(d) Find the direction of the displacement with respect to the eastward direction.
(e) How far and in what direction must the aircraft now fly to return straight to the airport?