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How do you start drawing a diagram in a problem with relative velocities? I always see my coursemates and my lecturer drawing them in a second, as soon as they read the text, I asked them how they did it, they just couldn't explain cause it just comes naturally. But to me it's very hard to figure out how to actually draw them as we are talking about different frames.

For example consider this problem river Now I draw this after a while, where $V_{bo}$ is the velocity of the boat wrt the ocean, $V_{og}$ is the velocity of the ocean wrt the ground, and $V_{bg}$ is the velocity of the boat wrt to the ground. But the diagram, it is quite random really, because I could have easily put the arrows in another order, but with the same direction! So for example I could have put the head of $V_{og}$ where $V_{bo}$ starts or other changes. enter image description here

How do I decide how to put the arrows? In "putting the arrows" I mean, how do I know I have to put $V_{og}$ starting point as the same of $V_{bo}$ and not put the head of the first, where the second starts? And what about where the second has its head?

Is it related to the formula $$V_{ab} = V_{ac} + V_{cb}$$ ? and if so how? I really struggle everytime to draw these diagrams and it takes me more than half an hour every time..

EDIT To show what I mean here's my drawing: triangles

As you can see it works fine most of the times. But if I follow the advice of connecting the heads or the tails of the two absolute velocities, I can get a different vector, as shown in the last two triangles of column 1, but you could get the same on the left side as well. Also, we don't know which of those triangle would be correct, or do we?

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The velocity of the boat relative to the ocean is the velocity of the boat minus the velocity of the ocean. The last two terms are what you are referring to as relative to the ground, or absolute velocities.

The vectors oney the triangular law of vector addition.

Draw a triangle so that the arrow heads of the two absolute velocities either converge at one point or both head away from one point.

The third side of the triangle is the relative velocity.

Follow the arrows to indicate the correct direction of the relative velocity.

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  • $\begingroup$ in your third paragraph "Draw a triangle so that..", how do I know whether they converge or diverge at one point? Like is my diagram correct? And if so, how do we know it is $\endgroup$
    – Euler_Salter
    Jan 15, 2017 at 1:44
  • $\begingroup$ You can draw two equally valid triangles. Either the absolute velocities point towards one point or they point both away from one point. In each case the third side is the relative velocity. I drew a picture but I don't seem to be able to upload the image - sorry. $\endgroup$
    – David Quinn
    Jan 15, 2017 at 10:27
  • $\begingroup$ okay that works of course, but there are other "degrees of freedom". In my diagram $V_{bg}$ and $V_{og}$ are the absolute velocities. From the text I know $V_{og}$ is vertical and pointing downwards. However I know nothing about $V_{bg}$. How do I decide at what angle they meet? For example in my photo I started from drawing $V_{og}$, then $V_{bo}$ with the angle $\phi$ with the vertical axis. But I could have never started from the two absolute velocities! Also, I have no way to check that my final diagram is correct, indeed I have no idea if mine is $\endgroup$
    – Euler_Salter
    Jan 15, 2017 at 10:39
  • $\begingroup$ Your diagram is not correct. The $v_{bo}$ and the $v_{bg}$ should be swapped over. The angles are unknown so it doesn't matter. $\endgroup$
    – David Quinn
    Jan 15, 2017 at 11:43
  • $\begingroup$ so now there's a problem with reality. If we have a current against us, in order to reach the same point, we have to have a bigger component in the same direction of the flow (so vertical), keeping the trasversal component the same (horizontal). And indeed in the diagram $v_{bg}$ has same horizontal component of $V_{bo}$ but bigger vertical component! How do you know they should be swapped over? Sorry I really struggle with this $\endgroup$
    – Euler_Salter
    Jan 15, 2017 at 11:57

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