Rather than the linear relationship of Eq. (1.7), you might choose to model the upward force on the parachutist as a second-order relationship, F_U = – c’v² where c’ = second-order drag coefficient (kg/m).

(a) Using calculus, obtain the closed-form solution for the case where the jumper is initially at rest (υ = 0 at t = 0).

(b) Repeat the numerical calculation in Example 1.2 with the same initial condition and parameter values. Use a value of 0.225 kg/m for c’.