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| <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | | <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> |
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| <p class="author"> | | <p class="author"> |
| Solutions of Savchenko Problems in Physics <br> | | Solutions of Savchenko Problems in Physics <br> |
| <i><b>knowledge must be free</b></i> | | <i><b>knowledge must be free</b></i> |
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| <h3 id="back-link"><a href="../../#1.3">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.3">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $1.3.12^*.$ From a hose lying on the ground, water shoots at an angle of $45^\circ$ to the horizon with an initial velocity of $10$ $\frac{m}{s}$. The cross-sectional area of the hose opening is $5$ $cm^2$ . Determine the mass of the jet in the air. | | $1.3.12^*.$ From a hose lying on the ground, water shoots at an angle of $45^\circ$ to the horizon with an initial velocity of $10$ $\frac{m}{s}$. The cross-sectional area of the hose opening is $5$ $cm^2$ . Determine the mass of the jet in the air. |
| </p> | | </p> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| <p>First, let's determine the flight time of each water drop. This time is:</p> | | <p>First, let's determine the flight time of each water drop. This time is:</p> |
| $$ t = \frac{2v_0 \cdot \sin \alpha}{g} $$ | | $$ t = \frac{2v_0 \cdot \sin \alpha}{g} $$ |
| <p>There is water in the air, flowing out of the hose in exactly time $t$. The mass of this water is easy to determine: it is the mass of water in a cylinder of height $v_0 t$ and base area $S$.</p> | | <p>There is water in the air, flowing out of the hose in exactly time $t$. The mass of this water is easy to determine: it is the mass of water in a cylinder of height $v_0 t$ and base area $S$.</p> |
| $$ m = \rho S v_0 t = \rho S \frac{2v_0^2 \cdot \sin \alpha}{g} $$ | | $$ m = \rho S v_0 t = \rho S \frac{2v_0^2 \cdot \sin \alpha}{g} $$ |
| | | |
| $$ m = \frac{2 \rho v_0^2 S \cdot \sin \alpha}{g} = 7.2 \text{ kg}. $$ | | $$ m = \frac{2 \rho v_0^2 S \cdot \sin \alpha}{g} = 7.2 \text{ kg}. $$ |
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