Question

Wind blows with a velocity x in the direction shown in Fig. Two aeroplanes start out from point $A$ and fly with a constant speed $y$. The first flies from $A$ to $B$ and the other along $A$ to$C$. Both of them return back to $A$. If $AB=AC$, then which plane will return to point $A$ first, and what will be the ratio of the times of flight of the two planes?

Answer 1

Time taken from $A$ to $B$ than $B$ to $A$

$t_{\left(AB/BA\right)}=\frac{AB}{y-x}+\frac{AB}{y+x}=\frac{2y\left(AB\right)}{y^2-x^2}$

Time taken from $A$ to $C$ than from $C$ to $A$

$t_{AC/CA}=\frac{2AC}{\sqrt{y^2-x^2}}R$

ratio of times$=\frac{y}{\sqrt{y^2-x^2}}=\frac{1}{\sqrt{1-x^2/y^2}}>1$

Hence, the first plane takes more time.