Updated spacing between @ latex expressions

astrosander edited
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revision #10313 parent #9246 GitHub c702ebe ← older newer →
en/1.3.16.md +6 −6
@@ -69,32 +69,32 @@
<p>a) Find the condition under which there will be no collisions$(x=0)$</p>
<p>From the law of conservation of energy:</p>
<p class="exp">
−$$ \frac{mv_0^2}{2} = mgl \cdot \sin \alpha $$
+$$ \frac{mv_0^2}{2} = mgl \cdot \sin\alpha$$
</p>
<p class="exp">
−$$ v_{0}\leq\frac{\sqrt{2gl\sin \alpha}}{\cos\alpha} $$
+$$ v_{0}\leq\frac{\sqrt{2gl\sin\alpha}}{\cos\alpha} $$
</p>
<p>In this case, time will pass</p>
<p class="exp">
−$$ t = \frac{2v_0}{g} \text{ctg} \alpha $$
+$$ t = \frac{2v_0}{g} \text{ctg} \alpha$$
</p>
<p>b) Now let's look at those cases when touching occurs:</p>
<p class="exp">
−$$ v_{0}>\frac{\sqrt{2gl\sin \alpha}}{\cos\alpha} $$
+$$ v_{0}>\frac{\sqrt{2gl\sin\alpha}}{\cos\alpha} $$
</p>
<p>Path between two touches:</p>
<p class="exp">
$$ L=v_{0}\cos\alpha t-\frac{g\sin\alpha t^{2}}{2} $$
</p>
<p>When we receive the required time, we choose the one that is smaller, because we need to find the time when it will come out</p>
<p class="exp">
−$$ t=\frac{v_{0}\cos\alpha-\sqrt{v_{0}^{2}\cos^{2}\alpha-2g\sin\alpha L}}{g\sin\alpha} $$
+$$ t=\frac{v_{0}\cos\alpha -\sqrt{v_{0}^{2}\cos^{2}\alpha -2g\sin\alpha L}}{g\sin\alpha} $$
</p>
</p>
<h4>Answer</h4>
<p>
− $\begin{aligned}&t=\frac{2v}{g}\operatorname{ctg}\alpha\text{ with }v\cos\alpha<\sqrt{2gl\sin\alpha};\\&t=\frac vg\operatorname{ctg}\alpha\bigg(1-\sqrt{1-\frac{2gl\operatorname{tg}\alpha}{v^2\cos\alpha}}\bigg)\text{ with }v\cos\alpha>\sqrt{2gl\sin\alpha}.\end{aligned}$
+ $\begin{aligned}&t=\frac{2v}{g}\operatorname{ctg}\alpha\text{ with }v\cos\alpha <\sqrt{2gl\sin\alpha};\\&t=\frac vg\operatorname{ctg}\alpha\bigg(1-\sqrt{1-\frac{2gl\operatorname{tg}\alpha}{v^2\cos\alpha}}\bigg)\text{ with }v\cos\alpha >\sqrt{2gl\sin\alpha}.\end{aligned}$
</p>
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