1. The velocity v(t) of a skydiver falling to the ground is governed by

mv = mg -kv²,

where m is the mass of the skydiver, g is the acceleration due to gravity, and k> 0 is a

constant related to the air resistance the diver faces.

a) Find the analytical solution for the skydiver's velocity v(t) as a function of time,

assuming that the initial velocity is v(0) = 0. You can use method of separation of variables.

b) Find the limiting value of v(t) as t→∞⁰.

(Strogatz: Nonlinear Dynamics and Chaos; pp. 38)