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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
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of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
$1.1.19.$ By what angle will the direction of velocity of the ball change after two elastic impacts on the walls, the angle between which is equal to $\alpha$? How will the ball fly if the angle $\alpha = \pi/2$? The motion occurs in a plane perpendicular to the walls. In an elastic collision with a smooth stationary wall, the angle of incidence of the ball is equal to the angle of reflection.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="250" />
<figcaption>
For problem $1.1.19$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
<p>
When falling elastically on a horizontal plane, the angle of incidence is equal to the angle of reflection.
</p>
<center>
<figure>
<img src="01.png" alt="1.1.19"
loading="lazy" width="400" />
<figcaption>
The point of intersection of the perpendiculars drawn on the edge of the angle
</figcaption>
</figure>
</center>
<p>
Thus, the direction of velocity of the ball after two elastic impacts will change by the angle $\beta = 2\alpha$
</p>
<p>
When $\alpha=\pi/2$, $\beta = \pi$, i.e., the ball will fly in the opposite direction..
</p>
</p>
<h4>Answer</h4>
<p>
$β = 2α$. In the direction opposite to the initial
<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">
<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
<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
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
$1.1.19.$ By what angle will the direction of velocity of the ball change after two elastic impacts on the walls, the angle between which is equal to $\alpha$? How will the ball fly if the angle $\alpha = \pi/2$? The motion occurs in a plane perpendicular to the walls. In an elastic collision with a smooth stationary wall, the angle of incidence of the ball is equal to the angle of reflection.
$1.1.19.$ By what angle will the direction of velocity of the ball change after two elastic impacts on the walls, the angle between which is equal to $\alpha$? How will the ball fly if the angle $\alpha = \pi/2$? The motion occurs in a plane perpendicular to the walls. In an elastic collision with a smooth stationary wall, the angle of incidence of the ball is equal to the angle of reflection.
</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 $1.1.19$
For problem $1.1.19$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>
<p>
When falling elastically on a horizontal plane, the angle of incidence is equal to the angle of reflection.
When falling elastically on a horizontal plane, the angle of incidence is equal to the angle of reflection.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="01.png" alt="1.1.19"
<img src="01.png" alt="1.1.19"
loading="lazy" width="400" />
loading="lazy" width="400" />
<figcaption>
<figcaption>
The point of intersection of the perpendiculars drawn on the edge of the angle
The point of intersection of the perpendiculars drawn on the edge of the angle
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Thus, the direction of velocity of the ball after two elastic impacts will change by the angle $\beta = 2\alpha$
Thus, the direction of velocity of the ball after two elastic impacts will change by the angle $\beta = 2\alpha$
</p>
</p>
<p>
<p>
When $\alpha=\pi/2$, $\beta = \pi$, i.e., the ball will fly in the opposite direction..
When $\alpha=\pi/2$, $\beta = \pi$, i.e., the ball will fly in the opposite direction..
</p>
</p>
</p>
</p>
<h4>Answer</h4>
<h4>Answer</h4>
<p>
<p>
$β = 2α$. In the direction opposite to the initial
$β = 2α$. In the direction opposite to the initial
<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>
