Answer
The height of the cliff is 225 feet.
Work Step by Step
$a(t) = \frac{dv}{dt} = -32$
$v(t) = \frac{ds}{dt} = v_0-32~t = -32~t$
$s(t) = s_0-16~t^2$
We can find the time $t$ it takes the stone to hit the ground:
$v(t) = -32~t = -120$
$t = \frac{120}{32}$
$t = 3.75~s$
We can find $s_0$:
$s(t) = s_0-16~t^2 = 0$
$s_0 = 16~t^2$
$s_0 = (16)(3.75)^2$
$s_0 = 225$
The height of the cliff is 225 feet.
