Question

how long does it take for a rock that is falling down from a distance of 200ft high?
what is the formula is used for this problem?

Answer 1

Note that an object falling freely experiences uniformly accelerated motion (UAM).
In this case, we can use the formula,
h = vo * t - (1/2) * g * t^2
where
h = height or distance
vo = initial velocity
t = time
g = acceleration due to gravity = 9.8 m/s^2 = 32.2 ft/s^2

Since the rock came from rest, the initial velocity (vo) is zero. The formula becomes,
h = - (1/2) * g * t^2
Substituting,
200 = -(1/2) * (-32.2) * t^2
200 = 16.1 * t^2
12.422 = t^2
t = 3.52 s
Note that the gravitational constant, 32.2, has a negative sign because it's direction is downward (acceleration in a vector quantity so its direction is important).

Hope this helps~ `u`