Question

An airplane flies northwards from town A to town B and then back again. There is a steady wind blowing to wards the north so that for the first stage of the trip, the airplane is flying in the same direction as the wind and for the return half of the journey, the airplane is flying directly into the wind. The total trip time T_w, as compared to the total trip time in the absence of any wind T_o, obeys: 

(A) T_w = T_o 

(B) T_w < T_o 

(C) T_w = 2T_o 

(D) T_w >T_o

Answer 1

For case I, Let wind speed is zero (for calculating T₀)

Then \(T_0=\frac{2d}{v_a}\) d is distance from A to B

For case II, Let wind speed be V_w

then T_w = \(\frac d{v_a+v_w}+\frac d{v_a-v_w}\)

\(=d(\frac{v_a-v_w+v_a+v_w}{v_a^2-v_w^2})\)

\(=\frac{2v_ad}{va^2-v_w^2}\) As speed of wind is too low

\(\therefore v_a^2>v_w^2\)

\(T_w=\frac{2v_ad}{va^2}=\frac{2d}{v_a}=T_0\)