A pilot is supposed to fly a certain distance `AB`, due east from `A to B` and then due west from `B to A`. The velocity of plane is `v` and that of air is `u`. The time for the round trip is `t_0` in still air. Show that
(a) if the air velocity be due east or west, the time for round trip will be `t_1 = (t_0)/((1 - (u^2)/(v^2))`.
(b) if the air velocity is due north or south, the time for a round trip will be `t_2 = (t_0)/sqrt((1 - (u^2)/(v^2)))`.
.

Explanation

`t_0 = (s)/(v) + (s)/(v) = (2 s)/(v)`
(a) `t = (s)/(v + u) +(s)/(v - u)=(2 s v)/(v^2 - u^2) = (v^2 t_0)/(v^2 - u^2) = (t_0)/(1 - u^2 //v^2)`
(b) `|vec v_1| = |vec v_2| = sqrt(v^2 - u^2)`
`t = (2 s)/(sqrt(v^2 - u^2))=(v t_0)/(sqrt(v^2 - u^2))= (t_0)/(sqrt(1 -(u^2)/(v^2)))`.
,.