4. In a water-filled and tightly sealed aquarium in the shape of a rectangular parallelepiped measuring 3 m $\times 4$ m $\times 2$ m, there are two small balls: an aluminum one and a wooden one. At the initial moment, the aquarium is at rest, and the distance between the balls is 2 m. What is the greatest distance between the balls that can be observed if the aquarium starts to move with constant acceleration? Provide an example of the motion in which the maximum distance is achieved.
4. The aluminum ball is heavier than water, so in a state of rest, it will occupy the lowest position, while the wooden ball is lighter than water, so it will occupy the highest position. Note that the distance between the balls in a state of rest is equal to the length of the shortest side. Therefore, the largest face is horizontal, and the balls are on the same vertical line.

If the aquarium starts to move with acceleration, the heavy ball "sinks," moving in the direction opposite to the acceleration, while the light ball "floats," moving in the direction of the acceleration. The maximum possible distance is the largest diagonal of the parallelepiped $\sqrt{3^{2}+4^{2}+2^{2}}=\sqrt{29}$. The balls will move apart to this distance during any uniformly accelerated motion of the aquarium, provided the acceleration is not parallel to one of the horizontal edges.