A rock is dropped off a cliff and strikes the ground with an impact velocity of $30\ \mathrm{\displaystyle \frac{m}{s}}$. How high was the cliff?
A) $20\ \mathrm{m}$
B) $30\ \mathrm{m}$
C) $45\ \mathrm{m}$
D) $60\ \mathrm{m}$
A) $20\ \mathrm{m}$
B) $30\ \mathrm{m}$
C) $45\ \mathrm{m}$
D) $60\ \mathrm{m}$
Use Big Five #5:
$$v^2={v_0}^2+2a(x-x_0)$$
with $v_0=0$ (calling down the positive direction):
$$v^2=2a(x-x_0)$$
$$(x-x_0)=\frac{\ v^2}{2a}$$
$$(x-x_0)=\frac{\ v^2}{2g}$$
$$(x-x_0)=\frac{\left(30\ \mathrm{\displaystyle \frac{m}{s}}\right)^2}{2\left(10\ \mathrm{\displaystyle \frac{m}{\ s^2}}\right)}$$
$$(x-x_0)=45\ \mathrm{m}$$