On a horizontal, frictionless surface, a cube of edge $d=10~ cm
$ vand of uniform mass distribution, is sliding at a velocity of $v_0$. At some point the cube reaches a slope of an angle of inclination of $\alpha=30^\circ$. The «fault line» between the slope and the ground is perpendicular to the direction of travel of the cube. The front edge of the cube which is in contact with the ground gets stuck at the fault line totally inelastically, so that the cube topples.

1 What is the least value of $v_0$ if the front face of the cube «tips» onto the slope?

2 What is the least value of $v_0$ if the front face of the cube loses contact with the surface before «tipping»?

3 What is the maximum distance achieved after «tipping» between the «fault line» and the leftmost point of the cube in contant with the inclined sufrace?