Translated 1.4.1-1.4.18
en/1.4.4.md
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| + | <head> | ||
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| + | <meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | ||
| + | <meta name="description" content="From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current."> | ||
| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current."> | ||
| + | <meta property="og:image" content="img/logo.png"> | ||
| + | <meta property="og:description" content="From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current."> | ||
| + | <meta name="yandex-verification" content="6cfda41f74038368"> | ||
| + | <title>From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current.</title> | ||
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| + | </head> | ||
| + | <body style=""> | ||
| + | <header style="text-align:center;"> | ||
| + | <h2>Solutions of Savchenko Problems in Physics</h2> | ||
| + | <p class="author"> | ||
| + | Aliaksandr Melnichenka <br/> | ||
| + | October 2023 | ||
| + | </p> | ||
| + | </header> | ||
| + | |||
| + | <h3 id="back-link"><a href="../../#1.4">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $1.4.4.$ From corner $A$ of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is $\frac{4}{3}$ of the speed of the river current. | ||
| + | </p> | ||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/1/1.4.4/statement.png" | ||
| + | loading="lazy" width="200" /> | ||
| + | <figcaption> | ||
| + | For problem $1.4.4$ | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | <p> | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | <p > | ||
| + | Let's consider the dog's movement relative to the shore | ||
| + | </p> | ||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/1/1.4.4/draw.png" | ||
| + | loading="lazy" width="150" /> | ||
| + | </figure> | ||
| + | </center> | ||
| + | |||
| + | <p > | ||
| + | On segment $AB$ the dog swims $4\, m$ vertically and is washed away $3\, m$ horizontally. | ||
| + | </p> | ||
| + | <p > | ||
| + | Next, on $BC$ the dog swims $4\, m$ horizontally along the river current and is washed away $3\, m$ in the same direction. | ||
| + | </p> | ||
| + | <p > | ||
| + | On $CD$ the dog swims $4\, m$ vertically, but in a different direction, and is again washed away $3\, m$ along the river current. </p> | ||
| + | <p > | ||
| + | On the last segment, the dog swims against the river current for $4\, m$, and the river washes away for $3\, m$, making a total movement of $1\, m$ against the river current. | ||
| + | </p> | ||
| + | |||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/1/1.4.4/ans.png" id="ans" | ||
| + | loading="lazy" width="300" /> | ||
| + | </figure> | ||
| + | </center> | ||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | <a href="#ans">See figure</a></h3> | ||
| + | </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> aliaksandr@savchenkosolutions.com <br></small> | ||
| + | </p> | ||
| + | </footer> | ||
| + | </body> | ||
| + | |||
| + | </html> | ||
| @@ -0,0 +1,112 @@ | |||
| <!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="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | |||
| <meta name="description" content="From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current."> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current."> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current."> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>From corner A of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is \frac{4}{3} of the speed of the river current.</title> | |||
| <link rel="stylesheet" href="https://savchenkosolutions.com/css/css-latex/style.css"> | |||
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| messageStyle: 'none' | |||
| }); | |||
| </script> | |||
| </head> | |||
| <body style=""> | |||
| <header style="text-align:center;"> | |||
| <h2>Solutions of Savchenko Problems in Physics</h2> | |||
| <p class="author"> | |||
| Aliaksandr Melnichenka <br/> | |||
| October 2023 | |||
| </p> | |||
| </header> | |||
| <h3 id="back-link"><a href="../../#1.4">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $1.4.4.$ From corner $A$ of a square raft, a dog jumped into the water and swam around the raft. Draw the dog's trajectory relative to the shore if it is swimming along the sides of the raft, and its speed relative to the water is $\frac{4}{3}$ of the speed of the river current. | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/1/1.4.4/statement.png" | |||
| loading="lazy" width="200" /> | |||
| <figcaption> | |||
| For problem $1.4.4$ | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <p> | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| <p > | |||
| Let's consider the dog's movement relative to the shore | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/1/1.4.4/draw.png" | |||
| loading="lazy" width="150" /> | |||
| </figure> | |||
| </center> | |||
| <p > | |||
| On segment $AB$ the dog swims $4\, m$ vertically and is washed away $3\, m$ horizontally. | |||
| </p> | |||
| <p > | |||
| Next, on $BC$ the dog swims $4\, m$ horizontally along the river current and is washed away $3\, m$ in the same direction. | |||
| </p> | |||
| <p > | |||
| On $CD$ the dog swims $4\, m$ vertically, but in a different direction, and is again washed away $3\, m$ along the river current. </p> | |||
| <p > | |||
| On the last segment, the dog swims against the river current for $4\, m$, and the river washes away for $3\, m$, making a total movement of $1\, m$ against the river current. | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/1/1.4.4/ans.png" id="ans" | |||
| loading="lazy" width="300" /> | |||
| </figure> | |||
| </center> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| <a href="#ans">See figure</a></h3> | |||
| </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> aliaksandr@savchenkosolutions.com <br></small> | |||
| </p> | |||
| </footer> | |||
| </body> | |||
| </html> | |||