(key Q15)

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bj Draw a graph that shows the height of the tide over a 24 h period, Assume that high tide is at 00:00 (midnight). MHF 4UB Unit Ill Workbook 37 4. c) What is the height at 10:00 (10:00 am)? d) At what times, over the 24 h period, is the height of the water 9 m? Estimate from your graph. KEY QUESTIONS Lesson 15 1. Application [4 marks] Another model for a bouncing ball is A() =4sin'(&ar) where h is height measured in metres and tis time in seconds. When is the first time the ball at a height of 2 m?MHF 4UB Unit Ill Workbook 38 2. State the equation of each sine function. [4 marks] (B amplitude of 3.5. D) period of phase shift of AMA 3. Knowledge/Understanding [3 marks] A weight is suspended on a spring. The weight is pulled down a distance of 30 om and released. The equation of the function that describes the motion of the spring is /(x) =30sin-" +60. State: 1.1 amplitude period vertical shift 3. Communication [5 marks] Describe how you obtain the equation in the form y = a sin k(x+c) + d for a sinusoidal function that has the following characteristics: amplitude 5 period 4TT a phase shift of w/4 to the right range -357 574. Applications (5 marks] A piston in a large factory engine moves up and down in a cylinder. The height, h centimetres, of the piston att seconds is given by the function hr) = 120sinar + 200. a) Amplitude = period = b) What are the maximum and minimum heights of the piston? c) How many complete cycles does the piston make in 30 min.7 5. Thinking/inquiry/Problem Solving [6 marks] The rodent population in a particular region varies with the number of predators that inhabit the region. At any time, one can predict the rodent population r() by using the function m() = 2500+1500sin -/, where t is the number of years that have passed since 1976. [A grid is provided for graphing to help in communicating your thinking.] a) In the first cycle (one complete wavelength) of this function, what was the maximum number of rodents and in which year did this occur? Explain your answer. b) What was the minimum number of rodents in a cycle? Explain your answer,c) What is the period of this function? d) How many rodents does this function predict for the year 20127 Journal Lesson 15 From personal experience or reading. describe an application of a periodic function. Reflect on your learning in this lesson