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Mechanics vector question

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.
IMG_0808.jpg162.6KB
IMG_0809.jpg191.3KB
Reply 1
Avatar for B_9710
B_9710
18
You should not have drawn the triangle with a right angle. You should draw just a general scalene triangle that deals with all cases.
(edited 7 years ago)
Reply 2
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tommy_lees
OP
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.
Reply 3
Avatar for B_9710
B_9710
18
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?
Reply 4
Avatar for tommy_lees
tommy_lees
OP
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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