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+ <meta name="description" content="The rope tied to the boat is pulled by the free end so that it does not sag. The boat moves at a constant speed v, forming at some point in time an angle \alpha with the length of rope located between the pole and the boat. How fast should the free end of the rope be pulled at this point in time?">
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+ <h2>Solutions of Savchenko Problems in Physics</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.5.13.$ The rope tied to the boat is pulled by the free end so that it does not sag. The boat moves at a constant speed $v$, forming at some point in time an angle $\alpha$ with the length of rope located between the pole and the boat. How fast should the free end of the rope be pulled at this point in time?
+</p>
+<center>
+ <figure>
+ <img src="https://savchenkosolutions.com/1/1.5.13/statement.png"
+ loading="lazy" width="210" />
+ <figcaption>
+ For problem $1.5.13$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <center>
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+ <img src="https://savchenkosolutions.com/1/1.5.13/draw.png"
+ loading="lazy" width="250" />
+ </figure>
+ </center>
+ <p>Если веревка не провисает, то</p>
+$$ \fbox{$u=\upsilon\cos\alpha$} $$
+<p>And since all points of the rope have the same speed, the rope must be pulled with exactly the speed $u$.</p>
+ </p>
+
+ <h4>Answer:
+ $u = v \cos \alpha$</h4>
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