Question

A stone is dropped from a cliff 100 ft. high. Disregarding friction;
a. how long does it take the stone to hit the ground?
b. With what speed and direction does it strike the ground?

Answer 1

a.
The stone is experiencing free fall, and therefore the motion involved is uniformly accelerated motion (UAM). We can use the formula,
h = vo*t - (1/2)gt^2
where
vo = initial velocity
t = time
g = acceleration due to gravity = 32.2 ft/s^2

Since it's free fall, vo = 0. Substituting,
100 = -(0.5)(-32.2)t^2
t = ?

Now solve for t.

b.
We can also use this formula for UAM:
vf^2 - vo^2 = 2gh
where
vf = final velocity

Terminal velocity is what we're looking for, and in this case it's vf since it's the velocity just before it hits the ground. Substituting the values,
vf^2 - 0 = 2(32.2)(100)

Now solve for vf. Note that the direction is downwards.

Hope this helps~ `u`