SOLUTION: a ferris wheel has a radius of 40 ft. there is an 8 ft clearance under the wheel for saftey. the wheel completes one rotation in 40 seconds. at what time does the rider first read

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Question 796627: a ferris wheel has a radius of 40 ft. there is an 8 ft clearance under the wheel for saftey. the wheel completes one rotation in 40 seconds. at what time does the rider first read a height of 60 ft?
the equation i came up with was h+=+-40cos+9t+%2B+48. then i got 60+=+-40cos+9t+%2B+48.
Answer by Alan3354(69443) About Me  (Show Source):
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a ferris wheel has a radius of 40 ft. there is an 8 ft clearance under the wheel for saftey. the wheel completes one rotation in 40 seconds. at what time does the rider first read a height of 60 ft?
the equation i came up with was h+=+-40cos+9t+%2B+48.
then i got 60+=+-40cos+9t+%2B+48
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Where did you get a 9?
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t = 0 at the bottom.
h(t) = 40*cos(t) give a period of 2pi and an amplitude of 40
h(t) = 40*cos(t*pi/20) changes the period to 40 seconds (t * 2pi/40)
h(t) = 40*cos(pi*t/20) + 48 shifts it up 48 feet.
h(t) = -40cos(pi*t/20) + 48 has it starting at the bottom of its cycle.
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at what time does the rider first read a height of 60 ft?
h(t) = -40cos(pi*t/20) + 48 = 60
-40cos(pi*t/20) = 12
cos(pi*t/20) = -3/10
pi*t/20 =~ 1.87549 radians
t =~ 11.94 seconds