Question

An airplane starts from A and flies to B at a constant speed. After reaching B it returns to A at the same speed. There was no wind. Assuming there was a wind from A to B of constant magnitude, when will the round trip take more time – when there is a wind or when there is no wind?

Answer 1

Answer:

When there is wind it takes longer

Explanation:

With no wind, the round trip time is

$t_1=\frac{d}{v}+\frac{d}{v}=\frac{2d}{v}$

When we have a constant wind speed w

$t_2=\frac{d}{v-w} +\frac{d}{v+w} =\frac{2vd}{v^{2} -w^{2}}$

comparing the reciprocal times;

$\frac{1}{t_2}=\frac{v^{2}-w^{2} }{2vd}=\frac{v}{2d}-\frac{w^{2}}{2vd} \leq \frac{v}{2d}=\frac{1}{t_1}$

This means that t1 is smaller than t2, ergo, it takes longer with wind