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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <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? | | $1.5.13.$ 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? |
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| For problem $1.5.13$ | | For problem $1.5.13$ |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| <p>Если веревка не провисает, то</p> | | <p>Если веревка не провисает, то</p> |
| $$ \fbox{$u=\upsilon\cos\alpha$} $$ | | $$ \fbox{$u=\upsilon\cos\alpha$} $$ |
| <p>And since all points of the rope have the same speed, the rope must be pulled with exactly the speed $u$.</p> | | <p>And since all points of the rope have the same speed, the rope must be pulled with exactly the speed $u$.</p> |
| </p> | | </p> |
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| <h4>Answer: | | <h4>Answer: |
| $u = v \cos \alpha$</h4> | | $u = v \cos \alpha$</h4> |
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