Find velocity with vector or without vector

AI Thread Summary
The discussion revolves around the confusion between vector and scalar representations of velocity in physics. The user initially equates velocity components in the x and y directions but struggles with the correct formulation of the overall velocity. It is clarified that the Pythagorean theorem applies only to right triangles, suggesting that the coordinates used may not represent a right triangle in space. The conversation also touches on the classification of Lagrange's Equations, indicating they are considered advanced rather than introductory physics. The thread was ultimately moved to a more appropriate forum for advanced topics.
Istiak
Messages
158
Reaction score
12
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.
 
Physics news on Phys.org
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.
 
robphy said:
By the way, I don't think Lagrange's Equations are considered "introductory physics" in this forum.
So, is that Advanced Physics? 🤔
 
Istiakshovon said:
So, is that Advanced Physics? 🤔
Yeah, for me at least, problems involving the Lagrangian qualify for the Advanced Physics schoolwork forum.

UPDATE -- Thread moved. :smile:
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'
(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
Back
Top