Chapter 1.3, Problem 4SP

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.

4. Julie pulls her ripcord 3000 ft. It takes 5 sec for her parachute to open completely and for her to slow down, during which time she falls another 400 ft. After her canopy is fully open, her speed is reduced to 16 ft/sec.

Find the total time Julie spends in the air, from the time she leaves the airplane until the time her feet touch the

ground. On Julie’s second jump of the day, she decides she wants to fall a little faster and orients herself in the “head down” position. Her terminal velocity in this position is 220 ft/sec. Answer these questions based on this velocity: