An object dropped near the surface of the earth experiences an approximatelyOriginally Posted by Greg E
constant acceleration of the minus sign is conventional as
up is normally taken as positive, and so downward accelleration is negative.
So , and if the initial speed is then .
Integrating again gives:
where is the initial height of the weight, for convenience we will
take this to be .
Now we are interested in what is happening when the weight has fallen
. This occurs when:
Putting this back into the equation for vertical velocity:
At the earth surface .
We could have short circuited this calculation by knowing that the change
in potential energy when the weight drops through a height is
which will equal the kinetic energy of the weight when it has fallen from rest
through a distance :