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# Mechanics vector question

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1. I wondering if anyone could help with this question:

An aircraft, whose speed in still air is v m/s, travels from a point A to a point B and back again. There is a wind of speed w m/s blowing in a direction making an angle theta to AB.

a) Show that the angle between the direction the aircraft steers and the direction in which it travels is the same for both stages of the journey..

b) Show that the journey is only possible if v > wsin theta.

I have attached what I have done some far, I just feel as though I am missing something.

Thanks in advance for any help.
Attached Images

2. You should not have drawn the triangle with a right angle. You should draw just a general scalene triangle that deals with all cases.
3. (Original post by B_9710)
You should not have drawn the triangle with a right angle. You should draw just a general scalene triangle that deals with all cases.
Thanks for looking at this.

For the first part I drew it as a scalene triangle. I then proved that the speed had to be the same if the angle between AB and the direction the aircraft steers was the same.

I could then draw it as a right angled triangle for the second part.
4. (Original post by tommy_lees)
Thanks for looking at this.

For the first part I drew it as a scalene triangle. I then proved that the speed had to be the same if the angle between AB and the direction the aircraft steers was the same.

I could then draw it as a right angled triangle for the second part.
Why did you draw it as a right angle though?
5. (Original post by B_9710)
Why did you draw it as a right angle though?
Good question. I drew it as a right angle triangle because otherwise the angle theta. (Between the line of travel and the line the plane is steering in) would not be equal.

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