A solid spherical ball of radius \(R=1.0 \mathrm{~cm}\) and mass \(M=2.0 \mathrm{~g}\) rolls, without crawling, on a horizontal plane with center-of-mass velocity equal to \(v_{0}=0.80 \mathrm{~m} / \mathrm{s}\). At the end of the plane the ball falls from a height \(h=0.60 \mathrm{~m}\) reaching the surface of a very large pool filled with water and 2.0 meters deep. Determine:

1. the point of impact with water with respect to the end of the plane;

2. the impact velocity of the ball when it enters the water;

3. the magnitude of the force called Archimedes' thrust, which is equal to the weight of the volume of water displaced by the ball when the ball is fully submerged (the direction of this force is opposite to that in which the weight force acts);

4. the acceleration in water of the ball; and 5. the maximum depth it reaches in the pool. Does it touch the bottom?

In addition to the transient phenomena of the ball entering and leaving the water, also neglect air friction, the viscosity/friction of the ball with the water, and the interaction of the ball with the edge.