# Aeroplane flight: time, displacement, velocity question

nathangrand
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?

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 