A raindrop falls through a cloud and accumulates mass at a rate kmv where k $=2$ m$1$

is a constant, m is the mass of the raindrop, and v its velocity.

$($a$)$ What is the speed of the raindrop at t $=10$ s if it starts from rest?

$($b$)$ What is its mass at t $=10$ s$?$ Assume that the initial mass of the raindrop is m$0=$

$10$ g$.$

Assume that a new raindrop falls through a cloud while accumulating mass at a rate r$2$

where r is its radius $($assume that the raindrop remains spherical$)$ and $=3$ kg$$m$2$s$.$

$($c$)$ Find its velocity at time t $=10$ s if it starts from rest with radius r$0=2$ cm$.$

$3$