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+ <meta name="description" content="A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?">
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+ <title>A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?</title>
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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="../../#1.5">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.5.4.$ A coin is placed on a wedge with an angle $\alpha$. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <p>During the time interval $t$, the coin changed its horizontal and vertical coordinates to $x$ and $y$, respectively</p>
+<center>
+<figure>
+<img src="https://savchenkosolutions.com/1/1.5.4/draw.png"
+loading="lazy" width="250" />
+<figcaption>
+Coin movement during the time interval $t$
+</figcaption>
+</figure>
+</center>
+<p>Considering the horizontal acceleration $a$ and the acceleration of gravity $g$, we find $x$ and $y$</p>
+<p class="exp">
+$$ x = \frac{at^2}{2} $$
+</p>
+ <p class="exp">
+$$ y = \frac{gt^2}{2} $$
+</p>
+<p>Considering that the body did not come off the wedge</p>
+<p class="exp">$$y = x \tan \alpha $$</p>
+<p>From where</p>
+<p class="exp">$$\fbox{$a = g \text{ ctg} \alpha $}$$</p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$a = g \text{ ctg} \alpha $$
+ </p>
+
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