<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
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<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
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master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
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of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
$1.1.12^*.$ Two rods intersect at an angle $2 \alpha$ and move with equal velocities $v$ perpendicular to themselves. What is the velocity of the intersection point of the rods?
</p>
<center>
<figure>
<img src="kin29.png"
loading="lazy" width="230" />
<figcaption>
For problem $1.1.12^*$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
<center>
<figure>
<img src="animation.gif"
loading="lazy" alt="1.1.12" width="80%" />
<figcaption>
Animation of rod movement
</figcaption>
</figure>
</center>
<p>
As shown in the animation, the intersection point will remain on the bisection of the angle $2\alpha$ between them as they move
</p>
<center>
<figure>
<img src="sol.png"
loading="lazy" alt="1.1.12" width="300" />
<figcaption>
Movement in a small amount of time
</figcaption>
</figure>
</center>
<p>
Consider the change of the intersection point on the horizontal axis during the time interval $dt$
</p>
<p>
From the geometry of a right triangle, the horizontal coordinate (aka hypotenuse) has changed to $dx = v dt / \sin\,\alpha$
<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
$1.1.12^*.$ Two rods intersect at an angle $2 \alpha$ and move with equal velocities $v$ perpendicular to themselves. What is the velocity of the intersection point of the rods?
$1.1.12^*.$ Two rods intersect at an angle $2 \alpha$ and move with equal velocities $v$ perpendicular to themselves. What is the velocity of the intersection point of the rods?
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="kin29.png"
<img src="kin29.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem $1.1.12^*$
For problem $1.1.12^*$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<center>
<center>
<figure>
<figure>
<img src="animation.gif"
<img src="animation.gif"
loading="lazy" alt="1.1.12" width="80%" />
loading="lazy" alt="1.1.12" width="80%" />
<figcaption>
<figcaption>
Animation of rod movement
Animation of rod movement
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
As shown in the animation, the intersection point will remain on the bisection of the angle $2\alpha$ between them as they move
As shown in the animation, the intersection point will remain on the bisection of the angle $2\alpha$ between them as they move
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="sol.png"
<img src="sol.png"
loading="lazy" alt="1.1.12" width="300" />
loading="lazy" alt="1.1.12" width="300" />
<figcaption>
<figcaption>
Movement in a small amount of time
Movement in a small amount of time
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Consider the change of the intersection point on the horizontal axis during the time interval $dt$
Consider the change of the intersection point on the horizontal axis during the time interval $dt$
</p>
</p>
<p>
<p>
From the geometry of a right triangle, the horizontal coordinate (aka hypotenuse) has changed to $dx = v dt / \sin\,\alpha$
From the geometry of a right triangle, the horizontal coordinate (aka hypotenuse) has changed to $dx = v dt / \sin\,\alpha$
<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>
