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<title>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?</title>
$1.1.20^*.$ 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>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="250" />
<figcaption>
For problem $1.1.20^*$
</figcaption>
</figure>
</center>
<p>
</p>
<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
<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>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
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<meta name="description" content="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
<meta name="description" content="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?">
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
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<meta property="og:description" content="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?">
<title>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?</title>
$1.1.20^*.$ 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>
<center>
<center>
<figure>
<figure>
<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>
</figure>
</figure>
</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;">
$\alpha = arctg (2ma/(nb))$
$\alpha = arctg (2ma/(nb))$
</p>
</p>
</p>
</p>
<h4>Answer</h4>
<h4>Answer</h4>
<p>
<p>
$\tan\alpha = 2ma/(nb)$, where $m$ and $n$ are any integers
$\tan\alpha = 2ma/(nb)$, where $m$ and $n$ are any integers
<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>
<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>
