Today in Precalculus Turn in graded worksheet Notes: Simulating circular motion – Ferris Wheels Homework

Example 1 1)Set up parametric equations that will form a circle x = cost y = sint 2) Change the amplitude for the radius of the Ferris wheel. x = 50cost y = 50sint 3) Adjust the y equation (the vertical equation) for the center of the wheel (vertical shift). x = 50cost y = 50sint + 65

Ferris Wheels 4) Include a phase shift so the wheel starts its rotation at the bottom (this will be the same for all equations) x = 50cos(t – π/2) y = 50sin(t – π/2) ) Change the period to reflect the time it takes for one revolution One revolution is 2π radians, so if it takes 18 seconds for one revolution then the period is 2π/18 or π/9 x = 50cos(π/9t – π/2) y = 50sin(π/9t – π/2) + 65

Ferris Wheels To view the graph: t: 0, at least 47 x: -60, 60 (greater than the radius on each side) y =0, 120 (at least diameter plus suspended height) (to see it as a circle, zoom – zsquare) Either trace graph, use table, or the equations to find position at 47 seconds. So they are ft to the left of center and ft high.

Example 2 Nikko is riding on a Ferris wheel that has a diameter of 122ft and is suspended so the bottom of the wheel is 12ft above the ground. The wheel makes one complete revolution every 20 seconds. Where is Nikko after 12 seconds? radius = 61 x = 61cos(2π/20t – π/2) = 61cos(π/10t – π/2) y = 61sin(2π/20t – π/2) + 73 = 61sin(π/10t – π/2) + 73 t: 0,20 x: -65,65 y: 0, 140 At 12 seconds, Nikko is feet to the left of center and feet high.

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