Chapter 1.3, Problem 6SP

A Parachutist in Free Fall

Figure 1.30 Skydivers can adjust [he velocity of their dive by changing the position of their body during the free fall. (credit: Jeremy T. Lock)

Julie is an avid skydiver. She has more than 30 jumps under her belt and has mastered the art of making adjustments

to her body position in the air to control how fast she falls. If she arches her back and points her belly toward the

ground, she reaches a terminal velocity of approximately 120 mph [176 ft/sec). If, instead, she orients her body with

her head straight down, she falls faster, leaching a terminal velocity of 150 mph (220 ft/sec).

Since Julie will be moving (falling) in a downward direction, we assume the downward direction is positive to simplify

our calculations. Julie executes her jumps from an altitude of 12,500 ft. After she exits the aircraft, she immediately

starts falling at a velocity given by v(t) = 32t. She continues to accelerate according to this velocity function until she

reaches terminal velocity. After she reaches terminal velocity, her speed remains constant until she pulls her ripcord

and slaws down In land.

On her first jump of the day, Julie orients herself in the slower "belly down” position (terminal velocity is 176 ft/sec).

Using this information, answer the following questions.

6. Before pulling her ripcord. Julie reorients her body in the “belly down” position so she is not moving quite as fast when her parachute opens. If she begins this maneuver at an altitude of 4000 ft. how long does she spend in a free fall before beginning the reorientation?

Some jumpers wear “wingsuits” (see Figure 1.31). These suits have fabric panels between the arms and legs and allow the wearer to glide around in a free fall, much like a flying squirrel. (Indeed, the suits are sometimes called flying squirrel suits.”) When wearing these suits, terminal velocity can be reduced to about 30 mph (44 ft/sec ), allowing the wearers a much longer tin in the air. Wingsuit flyers still use parachutes to land: although the vertical velocities are within the margin of safety, horizontal velocities can exceed 70 mph, much too fast to land safely.

Figure 1.31 The fabric panels on the arms and legs of a wingsuit work to reduce me vertical velocity of a skydiver’s fall. (credit: Richard Schneider)