Added en 1.1.3, 1.1.4; Updated GUI

astrosander правка от
Посмотреть решение История
правка #1773 GitHub a5e7c5b позже →
en/1.1.3.md +93 −0
@@ -0,0 +1,93 @@
+<!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>
+
+ <h3> Statement </h3>
+ <p>
+ $1.1.3.$ A bug flew into the room through an open window. The distance from the bug to the ceiling changed
+with a speed of 1 m/s, the distance to the wall opposite to the window changed with a speed of 2 m/s, to
+the side wall - with a speed of 2 m/s. After 1 s of flight the bug hit the corner between the ceiling and the
+side wall of the room. Determine the speed of the bug’s flight and the position in the window through
+which it flew into the room. The room is 2.5 m high, 4 m wide, and 4 m long.
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <p>
+ Let the beetle hit the corner $B$. It is known that after one second of flight the beetle has hit point $B$, so the window is at a distance of $1$ m from the ceiling, since with respect to the ceiling its velocity has changed by $1$ m/s.
+ </p>
+ <p>
+ Relative to the side wall, its velocity changed by $2$ m/s. Therefore, it flew at a distance of $2$ m from the side wall. Point $A$ is the place where the beetle flew into the room.
+ </p>
+ <p>
+ The coordinates of point $A$: $1$ m from the ceiling and $2$ m from the side wall. Knowing the change of velocities along the three directions $XYZ$, let's find the flight velocity of the beetle:
+ </p>
+ <p style="text-align: center;">
+ $$v = \sqrt{v_x^2 + v_y^2 + v_z^2}, \;(1)$$
+ </p>
+ <p>
+ Let's substitute the values of velocity projections into $(1)$
+ </p>
+ <p style="text-align: center;">
+ $$v = \sqrt{2^2 + 2^2 + 1^2} = 3 \; \frac{m}{s}$$
+ </p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ A beetle flew into the room at point $A$ located $1$ m from the ceiling and $2$ m from the side wall with a velocity of $3\, m/s$
+ </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>