# Find velocity with vector or without vector

• Istiak

#### 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.

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

UPDATE -- Thread moved. 