<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
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<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
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<meta name="description" content="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
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master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
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of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
$1.1.10^*.$ 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 $C$
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
<meta name="description" content="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
$1.1.10^*.$ 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 $u = v/2$.
$1.1.10^*.$ 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>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem $1.1.10^*$
For problem $1.1.10^*$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<center>
<center>
<figure>
<figure>
<img src="1.1.10.png" alt="1.1.10"
<img src="1.1.10.png" alt="1.1.10"
loading="lazy" width="200" />
loading="lazy" width="200" />
<figcaption>
<figcaption>
Chasing a bus
Chasing a bus
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<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: $AC = L, BC = h, AB = s.$
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>
</p>
<center>
<center>
<figure>
<figure>
<img src="sol.png" alt="1.1.10"
<img src="sol.png" alt="1.1.10"
loading="lazy" width="200" />
loading="lazy" width="200" />
<figcaption>
<figcaption>
The plane bounded by $\alpha$
The plane bounded by $\alpha$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
2. From right-angled triangle $ABC$ we have
2. From right-angled triangle $ABC$ we have
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$$L = s \cdot cos \frac{\alpha}{2}\text{ и }h = s \cdot sin \frac{\alpha}{2}$$
$$L = s \cdot cos \frac{\alpha}{2}\text{ и }h = s \cdot sin \frac{\alpha}{2}$$
</p>
</p>
<p>
<p>
3. Travel time of bus $t_1$ and passenger $t_2$ before meeting at point $C$
3. Travel time of bus $t_1$ and passenger $t_2$ before meeting at point $C$
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
