A skydiver of mass 80 kg falls vertically downward from rest
PHYSICS · Multi-part · ISC · Physics · Laws of Motion · Laws of Motion
Problem
A skydiver of mass 80 kg falls vertically downward from rest. The downward gravitational force is constant (magnitude mg), while the upward air-resistance force is proportional to the instantaneous velocity with proportionality constant k=14 kg/s. Motion is measured along a vertical axis with downward positive, and air density is assumed constant.
(a) Formulate the differential equation governing the velocity v(t) of the skydiver for t>0.
(b) Solve for v(t), and determine the limiting (terminal) velocity as t→∞.
(c) Obtain an expression for the displacement s(t) measured from the jump point, and compute the distance fallen after 12 seconds.
(d) Estimate the time required for the skydiver to fall the first 300 meters. Justify that your answer is consistent with the terminal velocity found in part (b).