Translated 1.3.3-1.3.15; Fixed GUI image generator

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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="../../#1.3">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.3.14.$ From the same place with a time interval of $\Delta t$, two bodies are thrown with the same initial velocity $v$ at an angle of $\varphi$ to the horizon. How does the first body move relative to the second? Why does the relative velocity depend only on $\Delta t$?
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <p>Before viewing the solution, I recommend viewing the solution to problem <a href="../1.3.1" target="_blank">1.3.1</a>.</p>
+<p>Over equal intervals of time, the vertical component of both velocities will decrease by an amount equal to $\Delta v_y = g \Delta t$, while the horizontal component $v_x$ remains unchanged. Therefore, their relative velocity will be constant and equal to the vector difference of the initial velocities.
+</p>
+<p>Subtracting each velocity component by component, we obtain that this relative velocity is (taking into account the equality $v_{x1} - v_{x2}$):
+</p>
+<p class="exp">
+$$v_{rel} = v_{y1} - v_{y2}$$
+</p>
+<p class="exp">
+$$\fbox{$v_{rel} = -g \Delta t$}$$
+</p>
+<p>Using the formulas obtained in <a href="../1.3.6" target="_blank">1.3.6</a>. By the time $\Delta t$, the first body will have relative coordinates:
+</p>
+<p class="exp">
+$$x_{{rel}}=(v\cos\varphi)\Delta t$$
+</p>
+<p class="exp">
+$$y_{{rel}}=(v\sin\varphi)\Delta t-g\Delta t^{2}/2$$
+</p>
+<p>Let's take into account the motion of the second body relative to the first over time:
+</p>
+<p class="exp">
+$$x_{{rel}}=(v\cos\varphi)\Delta t$$
+</p>
+<p class="exp">
+$$y_{{rel}}=(v\sin\varphi)\Delta t-g\Delta t^{2}/2 - g \Delta t$$
+</p>
+
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ <p>$x_{{rel}}=(v\cos\varphi)\Delta t;$ $y_{{rel}}=(v\sin\varphi)\Delta t$$-g\Delta t^{2}/2-g\Delta t\cdot t$, where $t$ is the time that has passed
+since the second body was ejected. The relative velocity is constant, directed vertically downwards
+and equal in absolute value to $g \Delta t$
+</p>
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