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 − kv^2, 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.) v(5) ≈ ft/s

(b) use separation of variables to solve the ivp and then find the actual value v(5). (round your answer to four decimal places.)