A stone falls from a ledge and takes 8 seconds to the hit the ground. the stone has an original velocity of 0 m/s. how tall is the ledge?

If it is moving at 0m/s then it isn't even moving ...

Using equation of motion.

S = ut + (1/2) gt²

Where S = Height, t = time, g = acceleration due to gravity = 9.8 m/s²

time, t = 8 seconds

Since it was dropped from height, initial velocity, u = 0

S = 0*t + (1/2) gt²

S = (1/2) gt²

S = (1/2) * 9.8*8² = 4.9 * 8 * 8 = 313.6

Therefore the ledge is 313.6 m tall.