Question

An airplane flies from a town $A$ to a town $B$ when there is no wind and takes a total time $T_0$ for a return trip. When there is a wind blowing in a direction from town $A$ to town $B$, the plane's time for a similar return trip, $T_W$ would satisfy

• A. $T_0<T_W$
• B. $T_0>T_W$
• C. $T_0=T_W$
• D. The result depends on the wind velocity between the towns

Answer 1

The correct option is A $T_0<T_W$

$\frac{2s}{v}=T_0$
$T_W=\frac{s}{v+v_W}+\frac{s}{v-v_W}=s\left[\frac{2v}{v^2-v_W^2}\right]=\frac{2s}{v}\left[\frac{v^2}{v^2-v_W^2}\right]$
$T_W=T_0\left[\frac{1}{1-{\left(\frac{v_W}{v}\right)}^2}\right]$