Updated spacing between @ latex expressions

astrosander edited
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revision #10491 parent #10016 GitHub c702ebe ← older newer →
en/1.5.17.md +9 −9
@@ -69,7 +69,7 @@
<p>NO: Before viewing the solution to this problem, I recommend that you familiarize yourself with the solution <a href="../1.5.16">1.5.16</a></p>
<p>At time $t$ the car will travel the distance $vt$ and the bottom will have horizontal coordinate $x$</p>
<p>
−$$ x = H \tan \alpha\quad(1) $$
+$$ x = H \tan\alpha\quad(1) $$
</p>
<p>Let's consider the change in angle $\alpha = \arctan \frac{H}{x}$ over a small period of time $dt$</p>
<p>
@@ -87,7 +87,7 @@
</p>
<p>Substitute $(1)$</p>
<p>
−$$ \omega = \frac{v}{H(1 + \tan^2 \alpha)} $$
+$$ \omega = \frac{v}{H(1 + \tan^2 \alpha )} $$
</p>
<p>
$$ \fbox{$\omega = \frac{v \sin^2 \alpha}{H}$} $$
@@ -97,7 +97,7 @@
<h3> Alternative solution: </h3>
<p>In time $\Delta t$ the truck will travel a distance</p>
<p>
−$$ \Delta l=\upsilon \Delta t $$
+$$ \Delta l=\upsilon\Delta t $$
</p>
<center>
<figure>
@@ -110,23 +110,23 @@
</center>
<p>The log will drop slightly, turning at a small angle $\Delta \alpha$. If the length of the arc of rotation is $\Delta x$, then by definition of the radian measure of angle</p>
<p>
−$$ \Delta \alpha=\frac{\Delta x }{R} $$
+$$ \Delta \alpha =\frac{\Delta x }{R} $$
</p>
<p>Angular velocity is defined as</p>
<p>
−$$ \omega=\frac{\Delta \alpha }{\Delta t }=\frac{\Delta x }{R\Delta t } $$
+$$ \omega =\frac{\Delta \alpha}{\Delta t }=\frac{\Delta x }{R\Delta t } $$
</p>
−<p>Но $\Delta x =\upsilon \Delta t\sin \alpha$.</p>
+<p>Но $\Delta x =\upsilon\Delta t\sin\alpha$.</p>
<p>
−$$ \omega=\frac{\upsilon \Delta t\sin \alpha }{R\Delta t }=\frac{\upsilon\sin \alpha }{R} $$
+$$ \omega =\frac{\upsilon\Delta t\sin\alpha}{R\Delta t }=\frac{\upsilon\sin\alpha}{R} $$
</p>
<p>We can also write that</p>
<p>
−$$ H=R\sin \alpha $$
+$$ H=R\sin\alpha$$
</p>
<p>With this in mind</p>
<p>
−$$ \omega=\frac{\upsilon\sin^2 \alpha}{H} $$
+$$ \omega =\frac{\upsilon\sin^2 \alpha}{H} $$
</p>
</p>
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