PhysicsLAB: Test Scenario: Drag Forces

Refer to the following information for the next five questions.

Terminal velocity is reached when a falling object's weight equals the air resistance it is encountering. That is, the object is in dynamic equilibrium.

The formula to directly calculate air resistance (AR) or drag is

where

ρ is the density of the medium through which the object is falling

A is the object's cross-sectional area being presented to the medium

C is the drag coefficient based on the object's shape

v_t is the object's terminal velocity

Six parachutists were released from a static line during a military exercise. The two screen captures shown above were taken 4 seconds apart during which time the red-square parachutist fell between the two marked vertical positions.

(a) If the jumper highlighted was 6-feet tall (1.8 meters) use proportions based on his actual height and his apparent length (height) in the photo to calculate the distance he fell in 4 seconds.

(b) Calculate the jumper’s terminal velocity.

(c) Given that the drag coefficient for the parachute was 1.12, the density of air was 1.225 kg/m3, and the jumper had a mass of 73 kg, calculate the cross-sectional area of the parachute after it was fully deployed.

(d) Calculate the parachute’s diameter.

(e) If a second parachutist was twice as massive (146 kg) what would be his terminal velocity if he used the same size parachute as in part (c)?