Updated greek laters @ latex compiling

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revision #9952 parent #9225 GitHub dbb31ba ← older newer →
en/1.3.13.md +3 −3
@@ -56,9 +56,9 @@
<h3>Solution</h3>
<p>
<p>a) We will use the formula for the flight path obtained in <a href="../1.3.6" target="_blank">1.3.6</a>:</p>
−$$ y(x) = x \tan \varphi-\frac{gx^2}{2v^2\cos^2\varphi} $$
+$$ y(x) = x \tan \varphi-\frac{gx^2}{2v^2\cos^2 \varphi} $$
<p>Let's use the <a href="#hint">hint</a>,</p>
−$$ y(x) = x \tan \varphi-\frac{gx^2}{2v^2}(1+\tan ^2 \varphi)\;(1) $$
+$$ y(x) = x \tan \varphi-\frac{gx^2}{2v^2}(1+\tan ^2 \varphi)\quad(1) $$
<p>Where do we express the angle $ \varphi$:</p>
$$ \tan \varphi=\frac{v^2\pm\sqrt{v^4-2gv^2y-g^2x^2}}{gx} $$
<p>b) Let's depict a set of trajectories, changing the angle $\varphi$ from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$:</p>
@@ -88,7 +88,7 @@
$$ v_x = v \sqrt{1-\xi ^2} $$
<p>Getting a function</p>
−$$ v(\xi)=\frac{\sqrt{g}x}{\sqrt{2 \xi \sqrt{1-\xi ^{2}}x-\xi ^{2}y}} \;(2) $$
+$$ v(\xi)=\frac{\sqrt{g}x}{\sqrt{2 \xi \sqrt{1-\xi ^{2}}x-\xi ^{2}y}} \quad(2) $$
<p>The maximum of the radical value corresponds to the minimum of the function (2)</p>
$$ (\sqrt{x^{2}+y^{2}-y})/2 \rightarrow \max $$
<p>Minimum of function $(2)$</p>
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