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I am stuck in a following question, the problem is that I am not understanding how to draw a picture of the following problem on a $Cartesian-Plane$.

Question: A small plane wishes to fly $due$ $north$ at $200$ $mph$ (as seen from the ground), in a wind blowing from the $northeast$ at $50$ $mph$. Tell with what $vector$ $velocity$ in the air it should travel (give the $i$ $j$$-$$components$).

Now there are following things confusing me while drawing the picture:

i) If the plane has to fly due north (as seen from the ground), then should I start the vector from Origin $O$ going to the north of the $Cartesian-Plane$ or start the vector from any point on $y-axis$ and take it to east?

ii) "wind blowing from the $northeast$", what does it mean? The wind is blowing from the direction 'North-East' to it's opposite direction or the wind is blowing from North to East? And how should I represent it's vector on the $Cartesian-Plane$?

iii) After making the vectors, would I need to find the components of the plane's vector in the direction of the wind's vector? Or I understood the question in wrong sense and I would have to do something-else?

Kindly help me in it by proper guiding me about which vector should go in which direction and from where it should be started? If possible try to make the proper image on paint and upload as an Answer or you can guide properly by writing the process of image-making in detail. This will help me a lot in understanding these types of questions. Thanks in advance.

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The wind is blowing from the north-east means it is blowing in the direction of south-west, i.e. on a bearing of $225^o$.

For the plane's velocity relative to the ground, draw an arrow going north of length 200. For the wind's velocity, draw an arrow of length 50 pointing towards the south-west. Draw these arrows to meet at one point. The third side of the triangle is the velocity of the plane relative to the wind, and this points in a direction east of North. Use the cosine rule and sine rule to solve.

Alternatively do everything in vector form:

$v_P=200j$ and $v_W=-\frac{50}{\sqrt{2}}(i+j)$

Then use the definition of relative velocity to get the velocity of the plane relative to the wind as $$_Pv_W=v_P-v_W$$

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  • $\begingroup$ thanks a lot for helping me to draw the image, but I need some more things to be cleared. The negative sign you used with the components of wind's vector, is it because the wind is blowing towards south-west direction and that makes it to go in the III-Quadrant of the plane where both x and y components are negative? $\endgroup$ Apr 18, 2017 at 14:21
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    $\begingroup$ Yes that's right $\endgroup$ Apr 18, 2017 at 16:10

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