Two towns A and B are separated by a distance D. An aircraft flying in still air between the two towns has a cruising speed of vp (with respect to the ground) and takes a time T for a round trip.
(a) Find an expression for T.
(b) If a wind vw blows from the west (i.e. to the east), find the time that the plane would take for a round trip from town A to B and back again. Show that it is greater than T.
(c) If a wind vw blows from the south (i.e. to the north), sketch a diagram showing the heading that the plane must fly so as to fly in a straight line from town A to town B. Again, find the round trip time for flying in such a cross wind.
(d) Show that regardless of the wind direction, the round trip time for a flight from town A to B and back again is longer than if there was no wind whatsoever. Find an expression for the round trip time if a wind vw blows in an arbitrary direction.