Student PROJECT 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 300 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, reaching 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 slows down to 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. 1. How long after she exits the aircraft does Julie reach terminal velocity? 2. Based on your answer to question 1, set up an expression involving one or more integrals that represents the distance Julie falls after 30 sec. 3. If Julie pulls her ripcord at an altitude of 3000 ft, how long does she spend in a free fall? 4. Julie pulls her ripcord at 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.

ple plot y A modern window has the shape of a rectangle topped by an equilateral triangle as shown in the image above. Find the dimensions of the window that allows the most light to pass through, if the outer perimeter of the window measures 8 m. Width of the window: x = Number m Height of the rectangular section: y Number FORMATTING: Give the answers with an accuracy of at least two decimal places.

F = C + 32° Use the formula above to find the Fahrenheit temperature equivalent to 95°C. А. 203°F В. 139°F C. 51°F D. 779°F 5

During a 4th of July celebration, your cousin, Bubba, lights two different rockets off his 14 ft roof at the same time from the same place. he two rockets follow these trajectories: Rocket #1: y = -0.41 +² +15t+14 Rocket #2: y = -0.31 +² + 14t+14 Where Y is the height (in feet) of the rockets t seconds after launch. (a) Which rocket goes higher, and how much higher? O Rocket #1 O Rocket #2 This higher rocket goes Number feet higher than the other. (round to one decimal place) (b) When do the rockets hit the ground? Rocket #1 will impact the ground after Number Rocket #2 will impact the ground after Number (c) Will the rockets crash into eachother? o Yes o No The rockets will crash into eachother after Enter 0 if they do not crash into eachother seconds. (round to one decimal place) seconds. (round to one decimal place) seconds. (round to one decimal place).