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<title>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.</title>
$1.1.19.$ 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
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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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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
<meta property="og:title" content="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.">
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<meta property="og:description" content="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.">
<title>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.</title>
$1.1.19.$ 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>
