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
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.
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:
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?
Best Answer
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.