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nathangrand
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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
Speed=distance/time
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?
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?
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