Savchenko Solutions

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.1.20^*.$ A ball is launched along a pool table with sides $a$ and $b$ from the middle of side $b$. At what angle to the side of the table must the ball begin to move to return to the same point from which it began its movement?

    <h3>Solution</h3>
    <p>
        
        <p>
          By analogy with <a href="/1.1.18">1.1.18</a>, we can use the Image Method and represent elastic walls as optical mirrors.  
        </p>
          <center>
          <figure>
            <img src="sol.png" alt="1.1.20" 
              loading="lazy" width="400" />
            <figcaption>
              Arrangement of image-dots
            </figcaption>
          </figure>
          </center>

        <p>
          To get to the starting position, all you have to do is hit any of the picture holes. 
        </p>
        <p>
          The coordinates of the holes are described by the expression: 
        </p>
        <p style="text-align: center;">
          $x=2ma$ и $y=nb$, где $m$ и $n$ — any integers
        </p>
        <p>
          Whence the desired angle:" 
        </p>
        <p style="text-align: center;">
          $\alpha = arctg (2ma/(nb))$ 
        </p>
        
    </p>

    <h4>Answer</h4>
    <p>
        $\tan \alpha = 2ma/(nb)$, where $m$ and $n$ are any integers
    </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>