Updated spacing between @ latex expressions

astrosander edited Oct 6, 2024, 12:48 AM

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en/1.5.4.md +7 −7

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		@@ -6,14 +6,14 @@
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		−	<meta name="description" content="A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
		+	<meta name="description" content="A coin is placed on a wedge with an angle \alpha . With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
			<meta name="author" content="Aliaksandr Melnichenka">
			<meta name="date" content="2023-10" scheme="YYYY-MM">
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		−	<meta property="og:description" content="A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
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		−	<title>A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?</title>
		+	<title>A coin is placed on a wedge with an angle \alpha . With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?</title>
			<link rel="stylesheet" href="../../css/css-latex/style.css">
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			extensions: ['tex2jax.js'],
			jax: ['input/TeX', 'output/HTML-CSS'],
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			<span><img src="../../img/book.png"></span><span>Savchenko Solutions</span>
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			<p class="author">
			Solutions of Savchenko Problems in Physics <br>
			<i><b>knowledge must be free</b></i>
			</p>
			</header>

			<h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3>

			<h3> Statement </h3>
			<p>
			$1.5.4.$ A coin is placed on a wedge with an angle $\alpha$. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?
			</p>

			<h3>Solution</h3>
			<p>
			<p>During the time interval $t$, the coin changed its horizontal and vertical coordinates to $x$ and $y$, respectively</p>
			<center>
			<figure>
			<img src="https://savchenkosolutions.com/1/1.5.4/draw.png"
			loading="lazy" width="250" />
			<figcaption>
			Coin movement during the time interval $t$
			</figcaption>
			</figure>
			</center>
			<p>Considering the horizontal acceleration $a$ and the acceleration of gravity $g$, we find $x$ and $y$</p>
			<p class="exp">
			$$ x = \frac{at^2}{2} $$
			</p>
			<p class="exp">
		@@ -73,14 +73,14 @@
			$$ y = \frac{gt^2}{2} $$
			</p>
			<p>Considering that the body did not come off the wedge</p>
		−	<p class="exp">$$y = x \tan \alpha $$</p>
		+	<p class="exp">$$y = x \tan\alpha$$</p>
			<p>From where</p>
		−	<p class="exp">$$\fbox{$a = g \text{ ctg} \alpha $}$$</p>
		+	<p class="exp">$$\fbox{$a = g \text{ ctg} \alpha$}$$</p>
			</p>

			<h4>Answer</h4>
			<p>
		−	$$a = g \text{ ctg} \alpha $$
		+	$$a = g \text{ ctg} \alpha$$
			</p>


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

	<head>		<head>
	<meta charset="utf-8">		<meta charset="utf-8">
	@@ -6,14 +6,14 @@
	<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="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">		<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
	<meta name="description" content="A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">		<meta name="description" content="A coin is placed on a wedge with an angle \alpha . With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
	<meta name="author" content="Aliaksandr Melnichenka">		<meta name="author" content="Aliaksandr Melnichenka">
	<meta name="date" content="2023-10" scheme="YYYY-MM">		<meta name="date" content="2023-10" scheme="YYYY-MM">
	<meta property="og:title" content="A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">		<meta property="og:title" content="A coin is placed on a wedge with an angle \alpha . With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
	<meta property="og:image" content="img/logo.png">		<meta property="og:image" content="img/logo.png">
	<meta property="og:description" content="A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">		<meta property="og:description" content="A coin is placed on a wedge with an angle \alpha . With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
	<meta name="yandex-verification" content="6cfda41f74038368">		<meta name="yandex-verification" content="6cfda41f74038368">
	<title>A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?</title>		<title>A coin is placed on a wedge with an angle \alpha . With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?</title>
	<link rel="stylesheet" href="../../css/css-latex/style.css">		<link rel="stylesheet" href="../../css/css-latex/style.css">
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	<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,
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	<a href="../../" style="text-decoration: none;">		<a href="../../" style="text-decoration: none;">
	<div id="logo">		<div id="logo">
	<span><img src="../../img/book.png"></span><span>Savchenko Solutions</span>		<span><img src="../../img/book.png"></span><span>Savchenko Solutions</span>
	</div>		</div>
	</a>		</a>
	<p class="author">		<p class="author">
	Solutions of Savchenko Problems in Physics <br>		Solutions of Savchenko Problems in Physics <br>
	<i><b>knowledge must be free</b></i>		<i><b>knowledge must be free</b></i>
	</p>		</p>
	</header>		</header>

	<h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3>		<h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3>

	<h3> Statement </h3>		<h3> Statement </h3>
	<p>		<p>
	$1.5.4.$ A coin is placed on a wedge with an angle $\alpha$. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?		$1.5.4.$ A coin is placed on a wedge with an angle $\alpha$. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?
	</p>		</p>

	<h3>Solution</h3>		<h3>Solution</h3>
	<p>		<p>
	<p>During the time interval $t$, the coin changed its horizontal and vertical coordinates to $x$ and $y$, respectively</p>		<p>During the time interval $t$, the coin changed its horizontal and vertical coordinates to $x$ and $y$, respectively</p>
	<center>		<center>
	<figure>		<figure>
	<img src="https://savchenkosolutions.com/1/1.5.4/draw.png"		<img src="https://savchenkosolutions.com/1/1.5.4/draw.png"
	loading="lazy" width="250" />		loading="lazy" width="250" />
	<figcaption>		<figcaption>
	Coin movement during the time interval $t$		Coin movement during the time interval $t$
	</figcaption>		</figcaption>
	</figure>		</figure>
	</center>		</center>
	<p>Considering the horizontal acceleration $a$ and the acceleration of gravity $g$, we find $x$ and $y$</p>		<p>Considering the horizontal acceleration $a$ and the acceleration of gravity $g$, we find $x$ and $y$</p>
	<p class="exp">		<p class="exp">
	$$ x = \frac{at^2}{2} $$		$$ x = \frac{at^2}{2} $$
	</p>		</p>
	<p class="exp">		<p class="exp">
	@@ -73,14 +73,14 @@
	$$ y = \frac{gt^2}{2} $$		$$ y = \frac{gt^2}{2} $$
	</p>		</p>
	<p>Considering that the body did not come off the wedge</p>		<p>Considering that the body did not come off the wedge</p>
	<p class="exp">$$y = x \tan \alpha $$</p>		<p class="exp">$$y = x \tan\alpha$$</p>
	<p>From where</p>		<p>From where</p>
	<p class="exp">$$\fbox{$a = g \text{ ctg} \alpha $}$$</p>		<p class="exp">$$\fbox{$a = g \text{ ctg} \alpha$}$$</p>
	</p>		</p>

	<h4>Answer</h4>		<h4>Answer</h4>
	<p>		<p>
	$$a = g \text{ ctg} \alpha $$		$$a = g \text{ ctg} \alpha$$
	</p>		</p>


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