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+ <header style="text-align:center;">
+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.1.10^*.$ A bus is driving along a straight highway at constant speed $v$. You have noticed the bus when it was at some point $A$. From what area near the highway can you catch up with this bus if your running speed is $u < v$? Draw this area for $u = v/2$.
+
+<center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" width="230" />
+ <figcaption>
+ For problem $1.1.10^*$
+ </figcaption>
+ </figure>
+</center>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+
+ <center>
+ <figure>
+ <img src="1.1.10.png" alt="1.1.10"
+ loading="lazy" width="200" />
+ <figcaption>
+ Chasing a bus
+ </figcaption>
+ </figure>
+ </center>
+
+ <p>
+ 1. Let the bus is at point $A$, and the catching up person starts from point $B$ and runs perpendicular to the roadway $AC$. Let us introduce the notations: $AC = L, BC = h, AB = s.$
+ </p>
+ <center>
+ <figure>
+ <img src="sol.png" alt="1.1.10"
+ loading="lazy" width="200" />
+ <figcaption>
+ The plane bounded by $\alpha$
+ </figcaption>
+ </figure>
+ </center>
+
+ <p>
+ 2. From right-angled triangle $ABC$ we have
+ </p>
+ <p style="text-align: center;">
+ $$L = s \cdot cos \frac{\alpha}{2}\text{ и }h = s \cdot sin \frac{\alpha}{2}$$
+ </p>
+ <p>
+ 3. Travel time of bus $t_1$ and passenger $t_2$ before meeting at point $C$
+ </p>
+ <p style="text-align: center;">
+ ${t}_{1}=\frac{{L}}{{v}}=\frac{{s}\cos(\alpha/2)}{{v}};\quad{t}_{2}=\frac{{h}}{{u}}=\frac{{s}\sin(\alpha/2)}{{u}}$
+ </p>
+ <p>
+ where from
+ </p>
+ <p style="text-align: center;">
+ $$\fbox{$\alpha = 2 \cdot \text{arcsin} \frac{u}{v}$}$$
+ </p>
+
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ From the region bounded by the angle $α = 2 \, \text{arcsin}(u/v)$ with vertex at the point $A$, bisected by the motorway
+ </p>
+
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