How is the position vector solved using arctan in the solution manual?

[ThatDude]

Homework Statement

2. The attempt at a solution

I would use the arctan (Position j / Position i) and set it equal to the position vector. Then I would substitute values from the graph to find the variables.

The solution manual, however, takes the derivative of the position vector and then sets it equal to the arctan (Position j / Position i). I don't understand the reasoning behind taking the velocity vector (derivative of position vector) instead of the position vector itself.

 

[BvU]

What is your question ?
What are the relevant equations ?
What is your attempt at solution ? Would this, would that ... is not what helps here. If you think that's the right way, then do it and show the results. Or perhaps you are by then convinced that your answer is right and the solution manual is in error (it happens, sometimes!).

 

[Chestermiller]

In this problem, they're using the symbol $\theta$ to represent the direction of the velocity vector, rather than the circumferential coordinate of the particle. This is an unfortunate choice, since it certainly causes confusion. They should have called it something else, like $\phi$.

Chet

 

[BvU]

Good point by Chet: I am one of the shallow readers who got confused...

 

[Chestermiller]

Good point by Chet: I am one of the shallow readers who got confused...

Don't beat yourself up. It was a poorly posed problem.

Chet