Suppose that velocity v of falling object satisfies given differential equation:
v'(t) =19.6 - v/40
i) Determine the number ve such that v(t) = ve is solution of equation (1) determine equilibrium solution of (1).
ii) Solve equation (1) with initial condition v(0) = 0. Determine limit of the solution when t is approaching infinity? How limiting velocity is related to answer in item (a)?
iii) Compute time which should elapse for object to reach 30% of limiting velocity found in item (ii).
iv) How far object falls in time found in item (iii).