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

When there is wind it takes longer

Step-by-step explanation:

With no wind, the round trip time is

`t_1=(d)/(v)+(d)/(v)=(2d)/(v)`

When we have a constant wind speed w

`t_2=(d)/(v-w) +(d)/(v+w) =(2vd)/(v^(2) -w^(2))`

comparing the reciprocal times;

`(1)/(t_2)=(v^(2)-w^(2) )/(2vd)=(v)/(2d)-(w^(2))/(2vd)   \leq (v)/(2d)=(1)/(t_1)`

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