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<meta name="description" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<meta property="og:title" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<title>Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?</title>
$1.1.12^*.$ 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="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<meta name="description" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<meta property="og:title" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<meta property="og:title" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<meta property="og:description" content="Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?">
<title>Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?</title>
<title>Two rods intersect at an angle 2 lpha and move with equal velocities v perpendicular to themselves. What is the velocity of the intersection point of the rods?</title>
$1.1.12^*.$ 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>
