How do I calculate how long it would take for something to fall (assume in a vacuum) from a certain height

IF the height is not high enough that the value of g (normally taken as 9.8 m/s²) to have changed by a significant amount, then you can use:
t = √(2h/g)

Above about 10-20 km, g is enough different that you get an error using the above equation, and it gets more complicated.

H = (1/2) g T²
=> T² = 2H / g
T = √(2H / g)
H = height, T = time taken, and g = acceleration due to gravity.
Formula applied : s = u t + (1/2) a t² , u = 0 ( for a falling body)

USING THE THREE EQUATIONS OF MOTION:

v = u+at
S = ut + 1/2a(t)^2
v^2 - u^2 = 2aS

a = acceleration
S = distance
v = final velocity
u = initial velocity
t = time period

h = 0.5 g t²


t² = 2h/ g

For example if h = 100 m

t²= 200/ 10
t = 4.47s
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