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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Solutions of Savchenko Problems in Physics
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    <h3 id="back-link"><a href="/#1.1">$\leftarrow$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?

    <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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