Question

A 3 kg rock sits on a 0.8 meter ledge. If it is pushed off, how fast will it be going at the bottom?

Answer 1

As long as it sits on the shelf, its potential energy
relative to the floor is . . .

   Potential energy =      (mass) x (gravity) x (height) =

                                       (3 kg) x (9.8 m/s²) x (0.8m) = 23.52 joules .

If it falls from the shelf and lands on the floor, then it has exactly that
same amount of energy when it hits the floor, only now the 23.52 joules
has changed to kinetic energy.

   Kinetic energy =                                          (1/2) x (mass) x (speed)²

                                                 23.52 joules = (1/2) x (3 kg) x (speed)²

Divide each side by  1.5 kg :     23.52 m²/s² = speed²

Take the square root of each side:    speed = √(23.52 m²/s²) =  4.85 m/s  (rounded)