An object is dropped onto the moon (g m = 5 ft/s 2). how long does it take to fall from an elevation of 250 ft.?

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.