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| <h3 id="back-link"><a href="../../#1.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.1">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <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. | | $1.1.19.$ 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. |
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| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" width="250" /> | | loading="lazy" width="250" /> |
| <figcaption> | | <figcaption> |
| For problem $1.1.19$ | | For problem $1.1.19$ |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
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| <p> | | <p> |
| </p> | | </p> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| | | |
| <p> | | <p> |
| When falling elastically on a horizontal plane, the angle of incidence is equal to the angle of reflection. | | When falling elastically on a horizontal plane, the angle of incidence is equal to the angle of reflection. |
| </p> | | </p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="01.png" alt="1.1.19" | | <img src="01.png" alt="1.1.19" |
| loading="lazy" width="400" /> | | loading="lazy" width="400" /> |
| <figcaption> | | <figcaption> |
| The point of intersection of the perpendiculars drawn on the edge of the angle | | The point of intersection of the perpendiculars drawn on the edge of the angle |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| | | |
| <p> | | <p> |
| Thus, the direction of velocity of the ball after two elastic impacts will change by the angle $\beta = 2\alpha$ | | Thus, the direction of velocity of the ball after two elastic impacts will change by the angle $\beta = 2\alpha$ |
| </p> | | </p> |
| <p> | | <p> |
| When $\alpha=\pi/2$, $\beta = \pi$, i.e., the ball will fly in the opposite direction.. | | When $\alpha=\pi/2$, $\beta = \pi$, i.e., the ball will fly in the opposite direction.. |
| </p> | | </p> |
| </p> | | </p> |
| | | |
| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $β = 2α$. In the direction opposite to the initial | | $β = 2α$. In the direction opposite to the initial |
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