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+ <header style="text-align:center;">
+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.1.12^*.$ 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 $dx = v dt / \sin\,\alpha$
+ </p>
+ <p>
+ From where the speed:
+ </p>
+ <p style="text-align: center;">
+ $$\fbox{$u = \frac{dx}{dt} = \frac{v}{\sin\,\alpha}$}$$
+ </p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$u = v/ \sin α$$
+ </p>
+
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