If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from m dv dt = mg − kv2, k > 0. Let v(0) = 0, k = 0.125, m = 8 slugs, and g = 32 ft/s2.
a. Use the RK4 method with h = 1 to approximate the velocity v(5). (Round your answer to three decimal places.)
b. Use separation of variables to solve the IVP and then find the actual value v(5). (Round your answer to four decimal places.)