During a manufacturing process, a liquid must be quickly transported from an upper level to a lower level of a factory by traveling in an open prismatic cart $($with a square base, aligned with the rails$)$ moving along straight rails inclined at an angle

$$

$=$

$2$

$2$

$$

$\backslash$alpha $=22$

$$

from the horizontal. The entire system is accelerated only by gravity, and the equivalent coefficient of friction between the rails and the cart is

$$

$=$

$0\mathrm{.}08$

$\backslash$mu $=0\mathrm{.}08.$ What is the minimum height the cart can have if its base has sides of length

$$

$=$

$1$

$$

m

a$=1$m and it is used to carry a volume of

$$

$=$

$2$

$$

m

$3$

V$=2$m

$3$

of liquid? The initial acceleration and final deceleration of the cart are not considered in this problem.

Hint: A minimum height is sought; what does this imply regarding the shape of the free surface?