To determine the time needed in order for the object to reach a certain elevation we use the equation,
d = V₀t + 1/2(gt²)
where d is the distance,
V₀ is the initial velocity which is equal to zero because the object is simply dropped
g is the acceleration due to gravity, and
t is the time
If we derive the equation in order to solve for t, we have,
t = sqrt ((2d/g))
If we convert the given in SI units,
d = (250 ft) x (0.3048 m/ 1 ft) = 76.2 m
g = (5 ft/s²)(0.3048 m/ 1 ft) = 1.524 m/s²
Substitute,
t = sqrt ((2)(76.2 m)/(1.524 m/s²))
t = 10 s
Therefore, it will take 10 s for the object to be dropped to a distance of 250 ft.
