Wile E. Coyote (mass = $40\ \mathrm{kg}$) falls off a 50‑meter‑high cliff. On the way down, the force of air resistance has an average strength of $100\ \mathrm{N}$.
Find the speed with which he crashes into the ground.
$v=27\ \mathrm{\displaystyle \frac{m}{s}}$
The force of air resistance opposes the downward motion, so it does negative work on the coyote as he falls:
$$W_{\mathrm{r}}=-F_{\mathrm{r}}h$$
Calling the ground $h=0$, we find that
$$k_{\mathrm{i}}+U_{\mathrm{i}}+W_{\mathrm{r}}=K_{\mathrm{f}}+U_{\mathrm{f}}$$
$$0+mgh+\left(-F_{\mathrm{r}}h\right)=\frac{1}{2}mv^2+0$$
$$v=\sqrt{2h\left(g-\displaystyle \frac{F_{\mathrm{r}}}{m}\right)}$$
$$v=\sqrt{2(50)\left(10-\displaystyle \frac{100}{40}\right)}$$
$$v=27\ \mathrm{\frac{m}{s}}$$