Find velocity with vector or without vector

[Istiak]

Homework Statement

Find velocity with vector or without vector

Relevant Equations

vector

At the moment he wrote that $\frac{1}{2}mv_2^2=\frac{1}{2}m(-\dot{y}+\dot{x})^2$

But, I know from vector $v_2=\sqrt{(-\dot{y})^2+(\dot{x})^2}$. At first I (he) found that $v_2=-\dot{y}+\dot{x}$. But, when thinking of simple velocity in $x$ and $y$ coordinate then I get $$v^2=\dot{x}^2+\dot{y}^2$$ (I remember the equation from my last book). What am I taking wrong with the top (absolute top) equation?

In the equation, $v_2=\sqrt{(-\dot{y})^2+(\dot{x})^2}$ if I square both side than I get the equation which I gave above. So, can we write that $v=\dot{x}+\dot{y}$. Then, if we square both side than that's simple algebraic expression. Maybe, this time I am mixing Algebra with Vector this time.

 

[robphy]

The Pythagorean theorem applies only to right-triangles.
In this problem, $x$ and $y$ are not the legs of a right-triangle in space,
and neither are $\dot x$ and $\dot y$.

The labels of the configuration coordinates are arbitrary.
Instead of the pair $x$ and $y$ (which is suggesting unrelated ideas),
use another pair (like $c$ and $d$).By the way, I don't think Lagrange's Equations are considered "introductory physics" in this forum.

 

[Istiak]

By the way, I don't think Lagrange's Equations are considered "introductory physics" in this forum.

So, is that Advanced Physics?

 

[berkeman]

So, is that Advanced Physics?

Yeah, for me at least, problems involving the Lagrangian qualify for the Advanced Physics schoolwork forum.

UPDATE -- Thread moved.