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# vectors watch

1. A bird has a speed in still air of 20 ms-1. It is pointed in the direction of the bearing 130 degrees, but there is a wind blowing at a speed of 10 m/s from the south west.

Take unit vectors i to point east and j to point north.

a) Express velocity of the bird relative to the air and the velocity w of the wind in compnent form, giving numerical values in ms-1 and the direction as a bearing to the nearest degree.

b) express resultant velocity v of the bird in componenet form , giving the numerical values in ms-1 to 2 d.p

c) hence find the magnitude and directon of the resultant velocity v of the bird, giving the magnitiude in ms-1 to 2 d.p and the direction as a bearing to the nearest degree.

I'm completely stuck. I do not understand it at all. Ive tried drawing a right handed triangle, and I've only managed to get wind velocity using 10cos45 i + 10 sin45 j...and I don't even know if thats right. I really need to be talked through this...
2. (Original post by aliceinwonder123)
...
Take the bird's velocity. We know that it is going at a speed of 20m/s in the direction of 130 degrees. So, draw your i and j axes. Measure 130 degrees from the +ve j axis clockwise, put a point down, and connect it to the origin. Draw the arrow to indicate direction of travel. Notice that it it moving in the +ve i direction but -ve j direction. So, then note that the angle between this vector and the +ve i axis is 40 degrees. Hence, the vector is ... ?
3. (Original post by RDKGames)
Take the bird's velocity. We know that it is going at a speed of 20m/s in the direction of 130 degrees. So, draw your i and j axes. Measure 130 degrees from the +ve j axis clockwise, put a point down, and connect it to the origin. Draw the arrow to indicate direction of travel. Notice that it it moving in the +ve i direction but -ve j direction. So, then note that the angle between this vector and the +ve i axis is 40 degrees. Hence, the vector is ... ?

is....320 degrees?

So I shouldnt have drawn a right handed triangle?

I dont know how to visualise the vectors. To be quite honest, I didnt understand how a direction of 130 degrees would look until you explain it in words.
4. (Original post by aliceinwonder123)
is....320 degrees
Not quite what I was going for...

The vector for bird's velocity is thus 20cos(40)i - 20sin(40)j

Diagram:
Spoiler:
Show

Now just repeat the same approach to obtain the velocity vector of the wind.

(Original post by aliceinwonder123)
I dont know how to visualise the vectors. To be quite honest, I didnt understand how a direction of 130 degrees would look until you explain it in words.
You should be OK with this because this is a GCSE topic that you would've done. If you're not, then I recommend you talk to your teacher so they can help you with the visualisation part and understand the bearing stuff.
5. (Original post by RDKGames)
Not quite what I was going for...

The vector for bird's velocity is thus 20cos(40)i - 20sin(40)j

Diagram:
Spoiler:
Show

Now just repeat the same approach to obtain the velocity vector of the wind.

You should be OK with this because this is a GCSE topic that you would've done. If you're not, then I recommend you talk to your teacher so they can help you with the visualisation part and understand the bearing stuff.
wow, thanks for the diagram. I wasnt getting anything near that. I have so many questions, but I guess i'll come back once I've learnt more.

Been 8 years since I've studied GCSE, and I really can't remember vectors.

One question,

will the wind velocity be a seperate diagram, or drawn on the same one?
6. (Original post by aliceinwonder123)
will the wind velocity be a seperate diagram, or drawn on the same one?
Doesn't matter, though part (b) would require you to draw both vectors on the same diagram for visual aid.

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Updated: February 6, 2018
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