# Aeroplane flight: time, displacement, velocity question

1. Homework Statement

An aeroplane makes a round trip between two airports A and B located on the same line of longitude. On a windless day the aeroplane travels with constant speed v and the round trip time is T0. On the following day the same journey is made but there is a wind blowing at speed kv (k<1) at an angle z to the line AB. The pilot maintains the same speed v relative to the air and always flies along the line AB and BA. The round trip time is now T (neglecting take offs, landings and stopovers)

Find T/T0

## Homework Equations

Speed=distance/time

## The Attempt at a Solution

Know that the distance for a round trip is vT0
Know that the speed will be different for A to B than B to A
Know that the answer is T/T0 = [(1-k^2(sin^2 z))^0.5]/(1-k^2)

When considering an angle of z=0 can get an answer of 1/(1-K^2) which is consistent with the above general answer

I just am not sure how to find the speeds relative to the ground with the wind at an angle?

tiny-tim
hi nathangrand! (try using the X2 icon just above the Reply box )
draw a vector triangle for each of the two journeys, then join the two triangles together and do a bit of trig 