Added en 1.1.4-1.1.10

astrosander правка от 26 авг. 2024 г., 03:51

правка #1778 предыдущая #1772 GitHub 0b9ce87 ← раньше позже →

en/1.1.4.md +1 −0

			<!DOCTYPE html>
			<html lang="en">

			<head>
			<meta charset="utf-8">
			<meta name="viewport" content="width=device-width, initial-scale=1.0">
			<meta http-equiv="content-language" content="en">
			<meta name="keywords" content="solutions, savchenko, physics problems, olympiad physics, physics book">
			<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
			<meta property="og:title" content="Savchenko Solutions">
			<meta property="og:image" content="img/logo.png">
			<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
			<meta name="yandex-verification" content="6cfda41f74038368">
			<title>Savchenko Solutions</title>
			<link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css">
			<link rel="icon" href="https://savchenko-physics.github.io/img/logo.png" type="image/png">
			<script src="https://savchenko-physics.github.io/js/jquery-1.10.1.min.js"></script>
			<script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"></script>
			<script type="text/x-mathjax-config">
			MathJax.Hub.Config({
			extensions: ['tex2jax.js'],
			jax: ['input/TeX', 'output/HTML-CSS'],
			tex2jax: {
			inlineMath: [['$', '$'], ['$', '$']],
			processEscapes: true,
			processClass: 'tex2jax',
			ignoreClass: 'html'
			},
			showProcessingMessages: false,
			messageStyle: 'none'
			});
			</script>
			</head>
			<body style="">
			<header style="text-align:center;">
			<h2>Solutions of Savchenko Physics Textbook</h2>
			<p class="author">
			Aliaksandr Melnichenka <br/>
			October 2023
			</p>
			</header>

			<h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>

		@@ -45,6 +45,7 @@
			<h3> Statement </h3>
			<p>
			$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?
		+
			<center>
			<figure>
			<img src="statement.png"
			loading="lazy" width="230" />
			<figcaption>
			For problem 1.1.4
			</figcaption>
			</figure>
			</center>
			</p>

			<h3>Solution</h3>
			<p>
			<p>
			1. Let us introduce the following variables
			</p>
			<p>
			$$x_B=L-x$$
			</p>
			<p>
			$$t_A=t_B+\Delta t$$
			</p>
			<p>
			2. Time of flight of $\gamma$-quantum to counters
			</p>
			<p>
			$$t_B+\Delta t=\frac{x}{c}$$
			</p>
			<p>
			$$t_B=\frac{L-x}{c}$$
			</p>
			<p>
			3. Solving the equations together, we obtain
			</p>
			<p>
			$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$
			</p>
			<p>
			$$x= \frac{L+c\Delta t}{2}=1.15\,м$$
			</p>
			</p>

			<h4>Answer</h4>
			<p>
			At a distance $1.15\, \text{m}$ from the microphone $A$
			</p>


			<footer class="row container">
			<br>
			<p>
			<small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
			</p>
			<p>
			<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
			</p>
			</footer>
			</body>

			</html>
		ещё строк без изменений 57

	<!DOCTYPE html>		<!DOCTYPE html>
	<html lang="en">		<html lang="en">

	<head>		<head>
	<meta charset="utf-8">		<meta charset="utf-8">
	<meta name="viewport" content="width=device-width, initial-scale=1.0">		<meta name="viewport" content="width=device-width, initial-scale=1.0">
	<meta http-equiv="content-language" content="en">		<meta http-equiv="content-language" content="en">
	<meta name="keywords" content="solutions, savchenko, physics problems, olympiad physics, physics book">		<meta name="keywords" content="solutions, savchenko, physics problems, olympiad physics, physics book">
	<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">		<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
	<meta property="og:title" content="Savchenko Solutions">		<meta property="og:title" content="Savchenko Solutions">
	<meta property="og:image" content="img/logo.png">		<meta property="og:image" content="img/logo.png">
	<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">		<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
	<meta name="yandex-verification" content="6cfda41f74038368">		<meta name="yandex-verification" content="6cfda41f74038368">
	<title>Savchenko Solutions</title>		<title>Savchenko Solutions</title>
	<link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css">		<link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css">
	<link rel="icon" href="https://savchenko-physics.github.io/img/logo.png" type="image/png">		<link rel="icon" href="https://savchenko-physics.github.io/img/logo.png" type="image/png">
	<script src="https://savchenko-physics.github.io/js/jquery-1.10.1.min.js"></script>		<script src="https://savchenko-physics.github.io/js/jquery-1.10.1.min.js"></script>
	<script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"></script>		<script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"></script>
	<script type="text/x-mathjax-config">		<script type="text/x-mathjax-config">
	MathJax.Hub.Config({		MathJax.Hub.Config({
	extensions: ['tex2jax.js'],		extensions: ['tex2jax.js'],
	jax: ['input/TeX', 'output/HTML-CSS'],		jax: ['input/TeX', 'output/HTML-CSS'],
	tex2jax: {		tex2jax: {
	inlineMath: [['$', '$'], ['$', '$']],		inlineMath: [['$', '$'], ['$', '$']],
	processEscapes: true,		processEscapes: true,
	processClass: 'tex2jax',		processClass: 'tex2jax',
	ignoreClass: 'html'		ignoreClass: 'html'
	},		},
	showProcessingMessages: false,		showProcessingMessages: false,
	messageStyle: 'none'		messageStyle: 'none'
	});		});
	</script>		</script>
	</head>		</head>
	<body style="">		<body style="">
	<header style="text-align:center;">		<header style="text-align:center;">
	<h2>Solutions of Savchenko Physics Textbook</h2>		<h2>Solutions of Savchenko Physics Textbook</h2>
	<p class="author">		<p class="author">
	Aliaksandr Melnichenka <br/>		Aliaksandr Melnichenka <br/>
	October 2023		October 2023
	</p>		</p>
	</header>		</header>

	<h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>		<h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>

	@@ -45,6 +45,7 @@
	<h3> Statement </h3>		<h3> Statement </h3>
	<p>		<p>
	$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?		$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?

	<center>		<center>
	<figure>		<figure>
	<img src="statement.png"		<img src="statement.png"
	loading="lazy" width="230" />		loading="lazy" width="230" />
	<figcaption>		<figcaption>
	For problem 1.1.4		For problem 1.1.4
	</figcaption>		</figcaption>
	</figure>		</figure>
	</center>		</center>
	</p>		</p>

	<h3>Solution</h3>		<h3>Solution</h3>
	<p>		<p>
	<p>		<p>
	1. Let us introduce the following variables		1. Let us introduce the following variables
	</p>		</p>
	<p>		<p>
	$$x_B=L-x$$		$$x_B=L-x$$
	</p>		</p>
	<p>		<p>
	$$t_A=t_B+\Delta t$$		$$t_A=t_B+\Delta t$$
	</p>		</p>
	<p>		<p>
	2. Time of flight of $\gamma$-quantum to counters		2. Time of flight of $\gamma$-quantum to counters
	</p>		</p>
	<p>		<p>
	$$t_B+\Delta t=\frac{x}{c}$$		$$t_B+\Delta t=\frac{x}{c}$$
	</p>		</p>
	<p>		<p>
	$$t_B=\frac{L-x}{c}$$		$$t_B=\frac{L-x}{c}$$
	</p>		</p>
	<p>		<p>
	3. Solving the equations together, we obtain		3. Solving the equations together, we obtain
	</p>		</p>
	<p>		<p>
	$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$		$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$
	</p>		</p>
	<p>		<p>
	$$x= \frac{L+c\Delta t}{2}=1.15\,м$$		$$x= \frac{L+c\Delta t}{2}=1.15\,м$$
	</p>		</p>
	</p>		</p>

	<h4>Answer</h4>		<h4>Answer</h4>
	<p>		<p>
	At a distance $1.15\, \text{m}$ from the microphone $A$		At a distance $1.15\, \text{m}$ from the microphone $A$
	</p>		</p>


	<footer class="row container">		<footer class="row container">
	<br>		<br>
	<p>		<p>
	<small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>		<small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
	</p>		</p>
	<p>		<p>
	<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>		<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
	</p>		</p>
	</footer>		</footer>
	</body>		</body>

	</html>		</html>
	ещё строк без изменений 57