$1.5.4.$ 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?
During the time interval $t$, the coin changed its horizontal and vertical coordinates to $x$ and $y$, respectively
Considering the horizontal acceleration $a$ and the acceleration of gravity $g$, we find $x$ and $y$
$$ x = \frac{at^2}{2} $$
$$ y = \frac{gt^2}{2} $$
Considering that the body did not come off the wedge
$$y = x \tan \alpha $$
From where
$$\fbox{$a = g \text{ ctg} \alpha $}$$
$$a = g \text{ ctg} \alpha $$