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.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.1.19.$ 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.

    <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
    </p>


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