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| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
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| + | <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> | ||
| + | $1.4.3.$ One of the dust cloud particles (particle $A$) is at rest, and all the others are flying away from it in different directions with velocities proportional to the distances from them to particle $A$. What motion pattern will an observer detect when moving with particle $B$? | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | <p > | ||
| + | He will find that all particles are moving away from him with a speed directly proportional to the distance from particle $B$ to them. | ||
| + | </p> | ||
| + | <p > | ||
| + | This can be proven as follows: write down the speeds of particle $B$ and an arbitrary particle $C$ in the reference frame of particle $A$, and then go to the reference frame of particle $B$, and make sure that the speed of particle $C$ in this reference frame is proportional to the distance between particles $B$ and $C$. Moreover, it is proportional with the same coefficient as in the reference frame of particle $A$. | ||
| + | </p> | ||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | Exactly the same as an observer moving with particle $A$. | ||
| + | </p> | ||
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| + | <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> | ||
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| @@ -0,0 +1,79 @@ | |||
| <!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="One of the dust cloud particles (particle A) is at rest, and all the others are flying away from it in different directions with velocities proportional to the distances from them to particle A. What motion pattern will an observer detect when moving with particle B?"> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="One of the dust cloud particles (particle A) is at rest, and all the others are flying away from it in different directions with velocities proportional to the distances from them to particle A. What motion pattern will an observer detect when moving with particle B?"> | |||
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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> | |||
| $1.4.3.$ One of the dust cloud particles (particle $A$) is at rest, and all the others are flying away from it in different directions with velocities proportional to the distances from them to particle $A$. What motion pattern will an observer detect when moving with particle $B$? | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| <p > | |||
| He will find that all particles are moving away from him with a speed directly proportional to the distance from particle $B$ to them. | |||
| </p> | |||
| <p > | |||
| This can be proven as follows: write down the speeds of particle $B$ and an arbitrary particle $C$ in the reference frame of particle $A$, and then go to the reference frame of particle $B$, and make sure that the speed of particle $C$ in this reference frame is proportional to the distance between particles $B$ and $C$. Moreover, it is proportional with the same coefficient as in the reference frame of particle $A$. | |||
| </p> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| Exactly the same as an observer moving with particle $A$. | |||
| </p> | |||
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| <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> | |||
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