Skydiver Luke jumps with his parachute of diameter D = 12m out of an airplane. The combined mass of the parachute and Luke is 100 kg. The drag coefficient for the fully open parachute is C_{D} = 1.4 . Neglecting acceleration and considering a linear change of air density with altitude, estimate Luke's fall time between altitudes of 3000 m and 2000 m. For the density of air at these two altitudes, assume pair (3000m) = 1.0 kg/m³ and pair (2000m) = 1.1 kg/m³.

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.