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| <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | | <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> |
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| <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="../../#1.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.1">$\leftarrow$Back</a></h3> |
| | | |
| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <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? | | $1.1.20^*.$ 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? |
| | | |
| </p> | | </p> |
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| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" width="250" /> | | loading="lazy" width="250" /> |
| <figcaption> | | <figcaption> |
| For problem $1.1.20^*$ | | For problem $1.1.20^*$ |
| </figcaption> | | </figcaption> |
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| </center> | | </center> |
| <p> | | <p> |
| </p> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| | | |
| <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. | | 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> | | </p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="sol.png" alt="1.1.20" | | <img src="sol.png" alt="1.1.20" |
| loading="lazy" width="400" /> | | loading="lazy" width="400" /> |
| <figcaption> | | <figcaption> |
| Arrangement of image-dots | | Arrangement of image-dots |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| | | |
| <p> | | <p> |
| To get to the starting position, all you have to do is hit any of the picture holes. | | To get to the starting position, all you have to do is hit any of the picture holes. |
| </p> | | </p> |
| <p> | | <p> |
| The coordinates of the holes are described by the expression: | | The coordinates of the holes are described by the expression: |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $x=2ma$ и $y=nb$, где $m$ и $n$ — any integers | | $x=2ma$ и $y=nb$, где $m$ и $n$ — any integers |
| </p> | | </p> |
| <p> | | <p> |
| Whence the desired angle:" | | Whence the desired angle:" |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $\alpha = \arctan (2ma/(nb))$ | | $\alpha = \arctan (2ma/(nb))$ |
| </p> | | </p> |
| | | |
| </p> | | </p> |
