m$($dv$)/($dt$)=$mg$-$kv

where k $>0$ is a constant of proportionality. The positive direction is downward.

plane is zero, that the air resistance is proportional to velocity, the acceleration due to gravity, g$,$ is $32$ft$//$s$^(2),$ and the positive direction is downward with s$(0)=0.$ See the figure.

What is the skydiver's velocity $($in ft$/$s$)21$ seconds after leaving the plane? $($Round your answer to two decimal places.$)$

ft$//$s

How far $($in feet$)$ has the skydiver traveled $21$ seconds after leaving the plane? $($Round your answer to two decimal places.$)$

How does the velocity at $21$ seconds compare with the skydiver's terminal velocity?

They have nearly reached their terminal velocity.

They are no where near their terminal velocity.

How long $($in minutes$)$ does it take the skydiver to reach the ground after exiting the plane? $($Hint: Think in terms of two distinct IVPs.$)($Round your answer to two decimal places.$)$