Chapter 1.3, Problem 2SP

A Parachutist in Free Fall

Figure 1.30 Skydivers can adjust the 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 question.

Based on your answer to previous question, set up an expression involving one or more integrals that represents the distance Julie falls after 30 sec.