Dynamics: Relative Acceleration

[Master1022]

Homework Statement

The problem is in the image attached below

2. Homework Equations

In the working below (although I think I have misunderstood a concept)

The Attempt at a Solution

My attempt is in the attached image.

I tried to leave the numbers out until the end. I have not written the exact working as I did it in draft elsewhere. I used the Law of Cosines on the vector triangle, in order to obtain $\vec v_{A/B}$, which came out as 2.057544... m/s. But that is not the correct answer.

Upon reflection, I have realized that I was supposed to draw the vector triangle such that the angle between $- \vec v_{B}$ and $\vec v_{A}$ is obtuse. How should one decide on how to draw the vector triangle?

Many thanks.

 

[TSny]

You need to construct $\vec a_A - \vec a_B$, which is the same as $\vec a_A + (- \vec a_B)$. So, your diagram should show $\vec a_A$ and $(- \vec a_B)$ added together.

 

[Master1022]

You need to construct $\vec a_A - \vec a_B$, which is the same as $\vec a_A + (- \vec a_B)$. So, your diagram should show $\vec a_A$ and $(- \vec a_B)$ added together.

Thanks for your response, it makes sense now.