# Finding velocity using Galilean Transformations

## Homework Statement

You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to a strong but steady wind) to maintain a northerly course you must point the nose of the plane at an angle of 22 west of true north. From previous flights on this route in the absence of wind, you know that it takes you 3.14 h to make the journey. With the wind blowing, you find that it takes 4.32 h. A fellow pilot calls to ask you about the wind velocity (magnitude and direction). What is your report?

## Homework Equations

V = L/t
V(prime) = V - U
Theta = invTan(U/V)

## The Attempt at a Solution

I have tried multiple ways to solve this prolem and have not even came close I dont believe. What I have done is taken 4.32 - 3.14 = 1.18 sec I figure that is the the amount of time added by the wind. I would assume the wind to be blowing south of east to counteract your angle. So then I said tan(22) = U/V which gives me V= U/tan(22) which gave me an answer of 1573 obviously incorrect. It also occured to me that maybe what I should have done was this get the velocity of the 4.32h time using V=L/T and also for the 3.14 using the same equation the subtract them and use them in the V = U/tan(22) that got me closer but it was still incorrect.

Andrew Mason
Homework Helper

## Homework Statement

You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to a strong but steady wind) to maintain a northerly course you must point the nose of the plane at an angle of 22 west of true north. From previous flights on this route in the absence of wind, you know that it takes you 3.14 h to make the journey. With the wind blowing, you find that it takes 4.32 h. A fellow pilot calls to ask you about the wind velocity (magnitude and direction). What is your report?

## Homework Equations

V = L/t
V(prime) = V - U
Theta = invTan(U/V)

## The Attempt at a Solution

I have tried multiple ways to solve this prolem and have not even came close I dont believe. What I have done is taken 4.32 - 3.14 = 1.18 sec I figure that is the the amount of time added by the wind. I would assume the wind to be blowing south of east to counteract your angle. So then I said tan(22) = U/V which gives me V= U/tan(22) which gave me an answer of 1573 obviously incorrect. It also occured to me that maybe what I should have done was this get the velocity of the 4.32h time using V=L/T and also for the 3.14 using the same equation the subtract them and use them in the V = U/tan(22) that got me closer but it was still incorrect.
Draw velocity vectors representing the velocity of the airplane relative to the air (A) and the velocity of the airplane relative to the ground (B). What do you do with these vectors to get the velocity vector for the air relative to the ground (C)?

Hint: You know A (750/3.14, N 22 W) and B (750/4.32, N). How do you get vector C from that?

AM

Thanks for the answer I figured it out woot!!