Estimate (a) how long it took king kong to fall straight down from the top of the empire state building (380 m high), and (b) the velocity just before "landing"

There are already derived equations for rectilinear motion at constant acceleration. For free falling objects, they are further simplified because only the gravitational force is acting on the body. The equations for time and velocity at impact are:

t = √2h/g
v = √2gh
where
h is the height
g is the acceleration due to gravity equal to 9.81 m/s²

1.  t = √2(380 m)/9.81 m/s² = 8.8 seconds
2.  v = √2(9.81 m/s²)(380 m) = 86.3 m/s