Centered 7 meters above the ground, a Ferris wheel of radius 6 meters is rotating with angular speed 24 degrees per second.
1 answer:
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.
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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