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| <h2>Solutions of Savchenko Problems in Physics</h2> | | <h2>Solutions of Savchenko Problems in Physics</h2> |
| <p class="author"> | | <p class="author"> |
| Aliaksandr Melnichenka <br/> | | Aliaksandr Melnichenka <br/> |
| October 2023 | | October 2023 |
| </p> | | </p> |
| </header> | | </header> |
| | | |
| <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> |
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| <p> | | <p> |
| $1.1.1.$ | | $1.1.1.$ |
| Figure$^{*)}$ shows a "blurred photograph" of a jet airplane in flight. The length of the airplane is 30 m, the length of its nose is 10 m. Determine | | Figure$^{*)}$ shows a "blurred photograph" of a jet airplane in flight. The length of the airplane is 30 m, the length of its nose is 10 m. Determine |
| from this "photograph" the speed of the airplane. The shutter exposure time is 0.1 s. The shape | | from this "photograph" the speed of the airplane. The shutter exposure time is 0.1 s. The shape |
| of the airplane is shown in the figure with a dashed line. | | of the airplane is shown in the figure with a dashed line. |
| </p> | | </p> |
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| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" alt="1.1.1" width="150" /> | | loading="lazy" alt="1.1.1" width="150" /> |
| <figcaption> | | <figcaption> |
| For the 1.1.1 problem | | For the 1.1.1 problem |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
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| <h4>Solution</h4> | | <h4>Solution</h4> |
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| <center> | | <center> |
| <figure> | | <figure> |
| <img src="1.1.1.png" | | <img src="1.1.1.png" |
| loading="lazy" alt="1.1.1" width="250" /> | | loading="lazy" alt="1.1.1" width="250" /> |
| <figcaption> | | <figcaption> |
| 1.1.1. Airplane photo | | 1.1.1. Airplane photo |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
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| <p> | | <p> |
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| To find the velocity of the airplane it is necessary to determine the vector of its displacement for the time $T$, during which the shutter of the camera is open. Let us select the initial point $1$ in the photograph and determine the distance it will move during the time $T$. The length of the airplane must be subtracted from the total length of the photograph. Taking into account the scale, the modulus of displacement will be | | To find the velocity of the airplane it is necessary to determine the vector of its displacement for the time $T$, during which the shutter of the camera is open. Let us select the initial point $1$ in the photograph and determine the distance it will move during the time $T$. The length of the airplane must be subtracted from the total length of the photograph. Taking into account the scale, the modulus of displacement will be |
| $$l=50-30 = 20 \;m$$ | | $$l=50-30 = 20 \;m$$ |
| For the 0.1 s aiplane covered a distance of $20\; m$, which corresponds to velosity of | | For the 0.1 s aiplane covered a distance of $20\; m$, which corresponds to velosity of |
| $$\boxed{v = \frac{l}{T} = 200\; m/s}$$ | | $$\boxed{v = \frac{l}{T} = 200\; m/s}$$ |
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