Challenge Problem Coaster Motion A wooden roller snider at Six Flags contains a run in the shape of a sinusoidal curve, with a series of hills. The crest of each hill is
that models the motion of the coaster train dining this run starting at the top of a hill.
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Precalculus
- Motion of a Projectile If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation (see Figure 10), then the height h of the projectile at time t is given by h=16t2+vtsin Give the equation for the height, if v is 1,500 feet per second and is 30.arrow_forwardPredator Population When two species interact in a predator/prey relationship, the populations of both species tend to vary in a sinusoidal fashion. See Discovery Project: Predator/Prey Models referenced on page 529. In a certain Midwestern county, the main food source for barn owls consists of field mice and other small mammals. The table gives the population of barn owls in this county every July 1 over a 12-year period. a Make a scatter plot of the data. b Find a sine curve that models the data as in Example 1. c Graph the function you found in part b together with the scatter plot. d Use a graphing calculator to find the sine curve that best fits the data as in Example 2. Compare to your answer from part b. Year Owl population 0 50 1 62 2 73 3 80 4 71 5 60 6 51 7 43 8 29 9 20 10 28 11 41 12 49arrow_forwardBlood Pressure The pressure P (in millimeters of mercury) against the walls of the blood vessels of a patient is modeled by P=10020cos8t3 where t is the time (in seconds). (a) Use a graphing utility to graph the model. (b) What is the period of the model? What does it represent in the context of the problem? (c) What is the amplitude of the model? What does it represent in the context of the problem? (d) If one cycle of this model is equivalent to one heartbeat, what is the pulse of the patient? (e) A physician wants the patient’s pulse rate to be 64 beats per minute or less. What should the period be? What should the coefficient of t be?arrow_forward
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