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

The height of a falling object, h, in terms of the seconds passed, t, is
h = 0.5(-9.8t^2) + v_0t + h_0
0 = -4.9(8)^2 + 0 + h_0
h_0 = 64 * 4.9
= 313.6 meters

Here's a formula that tells the distance covered by an
accelerating object starting from rest.  The formula is
very useful, and it's simple enough to memorize:

       Distance = (1/2) (acceleration) (time squared) .

If the object is falling, then the acceleration is gravity, 9.8 m/s²,
and the distance is

                         (4.9) (time²) .

In this question,

                     D  =  (4.9) (8²)

                         =  (4.9 x 64)  =  313.6 meters.

Coupla comments:

-- This calculation ignores air resistance. 
    We kind of ALWAYS do that, otherwise
    the calculation would be very complicated,
    and would need a lot of other numbers
    that we don't know, like the size and shape
    of the falling object, and the density of the air.

--  This is a very big building ... about 1,029 feet.
     In New York City, the Chrysler building and
     the New York Times building are both only
     15 feet taller than that.