Here comes Wonder-Blunder-Berg

Classical Mechanics Level 4

Inside a train moving at $0.5c$ (according to a bunch of people standing on the platform), a man holds a yard stick making an angle of $\frac{\pi}{6}$ with the horizontal (according to him).

What, in radians, is the angle he is making with the horizontal, according to the people on the platform?

The answer is 0.588003.

1 solution

Miloje Đukanović
Oct 26, 2015

$l_x=l_0\cos{\phi}$

$l_y=l_0\sin{\phi}$

$\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$l_x^{'}=\gamma l_0\cos{\phi}\quad\quad \color{#3D99F6}{\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}}$

$l_y^{'}=l_y=l_0\sin{\phi}$

$\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\tan{\phi^{'}}=\frac{l_y^{'}}{l_x^{'}}=\frac{2}{3}$

$\phi^{'}=\arctan{\frac{2}{3}}$

$\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\boxed{\phi^{'}\approx0.588}$

A good solution usually explains what the symbols mean.

Agnishom Chattopadhyay - 5 years, 7 months ago

A good solution always explains what the symbols mean.

Jake Lai - 5 years, 6 months ago

My solution is good, it doesn't explain what the symbols mean, from this we can conclude that your statement is incorrect.

Miloje Đukanović - 5 years, 6 months ago

@Miloje Đukanović – A solution is good if it is enjoyable, readable and helpful.

Calvin has a good note on that

Agnishom Chattopadhyay - 5 years, 6 months ago

@Miloje Đukanović – Your solution is undoubtedly correct, but a solution writer has to keep their audience in mind. What if a problem solver gets the question wrong as she does not understand/know concepts that you have used in your solution, like length contraction? These are key points to consider when writing a friendly and helpful solution.

I hope that you'll revise your solution with the intent that it will serve as a guiding step for keen but yet unversed learners in the community. Happy solving :)

Jake Lai - 5 years, 6 months ago

Here comes Wonder-Blunder-Berg

The answer is 0.588003.

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