At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver’s shoulders is given by x(t), and the vertical distance from the water surface to her shoulders is given by y(t), where x(t) and y(t) are measured in meters. The figure above shows the initial position of the diver and her position at a later time. A diver leaps from the edge of a diving platform into a pool below. (BC 2009 Exam #3 Figure 1) Note: Figure not drawn to scale. (d) On average, how long does a person wait in the auditorium for the concert to being? Consider all people who enter the auditorium after the doors open, and use the model for total wait time from part (c). Find w(2) – w(1), the total wait time for those who enter the auditorium after time t = 1. The derivative of w Is given by w’(t) = (2 – t) R(t). The function w models the total wait time for all the people who enter the auditorium before time t. (c) The total wait time for all people in the auditorium is found by adding the time each person waits, starting at the time the person enters the auditorium and ending when the concert beings. (a) How many people are in the auditorium when the concert begins? (b) Find the time when the rate at which people enter the auditorium is a maximum. The doors close and the concert beings at time t = 2. No one is in the auditorium at time t = 0, when the doors open. The rate at which people enter an auditorium for a rock concert is modeled by the function R given by R(t) = 1380t2 – 675t3 for 0 ≤ t ≤ 2 hours R(t) is measured in people per hour. Who lives closer to school: Caren or Larry? Show the work that leads to your answer.Ģ. His velocity is modeled by the function w given by w(t) = (π/15) sin (πt/12), where w(t) is in miles per minute for 0 ≤ t ≤ 12 minutes. (d) Larry also rides his bicycle along a straight road from home to school in 12 minutes. At what time does she turn around to go back home? Give a reason for your answer. Caren realizes she left her calculus homework at home, and she returns to get it. (b) Using correct units, explain the meaning of ∫(0 to 12) |v(t)| dt in terms of Caren’s trip. (a) Find the acceleration of Caren’s bicycle at time t = 7.5 minutes.
During the time interval 0 ≤ t ≤ 12 minutes, her velocity v(t), in miles per minute, is modeled by the piecewise-linear function whose graph is shown above. Caren rides her bicycle along a straight road from home to school, staring at home at time t = 0 minutes and arriving at school at time t = 12 minutes. 2009 AP Calculus BC Free-Response Questions Section II, Part A A graphing calculator is required for some problems or parts of problems.
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