Question

2. An airplane flies northward from towna A to B and then back again.T here is a steady wind blowing towards the north so that for the first stage of the trip, the airplane is flying in the same direction as the wind and for return trip of the journey, the airplane is flying directly into the wind. The total trip time Tw ,as compared to the total trip time iin the absence of any wind To.
(A)Tw=To (b) Tw>To
(c) Tw< To (d) Tw=2To

Answer 1

Dear Student,
$$\begin{gathered} letspeedofwindisuandofplaneisv \\ whenthereisnowindthen{T}_0=2\frac{d}{v} \\ whenwindisavailablethen \\ {T}_1=\frac{d}{v-u}---1 \\ {T}_2=\frac{d}{v+u}---2 \\ so{T}_w=\frac{d}{v-u}+\frac{d}{v+u}=d\left(\frac{1}{v-u}+\frac{1}{v+u}\right)=d\left(\frac{2v}{(v-u)(v+u)}\right)=\frac{2vd}{v^2-u^2} \\ =\frac{2\frac{d}{v}}{1-(\frac{u}{v}{)}^2} \\ heredenomenatorpartislessthanoneasu<v \\ so{T}_w>T_0 \end{gathered}$$
Regard