Chapter 5, Problem 102GP

(III) The force of air resistance (drag force) on a rapidly falling body such as a skydiver has the form F_D = −kv², so that Newton’s second law applied to such an object is

$m\frac{dv}{dt}=mg-k{v}^2.$

where the downward direction is taken to be positive. (a) Use numerical integration (Section 2–9] to estimate (within 2%) the position, speed, and acceleraton, from t = 0 up to t = 15.0 s, for a 75-kg skydiver who starts from rest, assuming k = 0.22 kg/m. (b) Show that the diver eventually reaches a steady speed, the terminal speed, and explain why this happens, (c) How long does it take for the skydiver to reach 99.5% of the terminal speed?