As a raindrop falls, it evaporates while retaining its spherical shape. Let's assume the rate at which the raindrop evaporates is proportional to its surface area and air resistance is negligible, a model for the velocity $v(t)$ is given as

$v^{\text{'}}\frac{3(\frac{k}{})}{\frac{k}{}t{r}_0}v=g$

So $$ will be the density of water, $r_0$ is given as the radius of the raindrop at $t=0,g$ is the gravitational constant, and $k($which will be less than $0)$ is the constant of proportionality. If the radius $r_0$ is given as $\mathrm{.}02$ ft $.$ Find the general solution of the velocity of the raindrop $v(t).{?}^{******}$ This will be a somewhat tricky process as you will

$1$

Problem Set $2$

MTH$2251$

Due : February $13,2025$

need to employ the linear equations method with reminding yourself that $k,g,$ and $$

will be treated as constant.