Centered 7 meters above the ground, a ferris wheel of radius 6 meters is rotating with angular speed 24 degrees per second. a. assuming that you begin at time t = 0 seconds at the lowest point on the wheel, find a formula that describes the distance h (in meters) from you to the ground after t seconds of riding. b. at what times are you 10 meters above the ground? explain clearly how you got your solution.

24 degrees per second is 360 degrees in 15 seconds (pretty fast for a Ferris wheel!).

a) The distance above the ground can be modeled using a cosine function.
.. h(t) = 7 -6cos(2πt/15)

b) h(t) = 10
.. 10 = 7 -6cos(2πt/15)
.. (10 -7)/-6 = cos(2πt/15)
.. 2πt/15 = π ±π/3 +2kπ
. t = 7.5*((1 ±1/3) +2k) . . . . . . . . seconds; k = any integer

You are 10 meters above the ground at t=5 seconds and every 15 seconds thereafter, as well as at t=10 seconds and every 15 seconds thereafter.

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