SOLUTION: Anna rides a Ferris wheel at a county fair. At time t=0, Anna is at a height of 5 feet from the ground which is the minimum height of the Ferris wheel. The center of the Ferris Whe

Algebra ->  Length-and-distance -> SOLUTION: Anna rides a Ferris wheel at a county fair. At time t=0, Anna is at a height of 5 feet from the ground which is the minimum height of the Ferris wheel. The center of the Ferris Whe      Log On


   

Question 1083859: Anna rides a Ferris wheel at a county fair. At time t=0, Anna is at a height of 5 feet from the ground which is the minimum height of the Ferris wheel. The center of the Ferris Wheel is at a height of 85 feet. The Ferris Wheel rotates at a constant speed and makes two complete turns during the six minutes that Anna is on the Ferris Wheel.
Part A:
Write a trigonometric function for h(t) to express Anna's height, in feet, in terms of time, t, in minutes. Explain how you determined you answer.
Part B:
Determine Anna's height, in feet at time t= 1 minute
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general formula for a cosine function is:
+h%28t%29+=+A%2Acos%28+B%2At+%2B+C+%29+%2B+D+
+abs%28A%29+ is the amplitude
+C%2FB+ is the phase shift
+%28+2%2Api+%29%2Fabs%28+B+%29+ = period
+abs%28+D+%29+ is the vertical shift
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(A)
The plot of a point that is a minimum at +t=0+
and then goes to a maximum and back to a
minimum would be a negative cosine function:
+h%28t%29+=+-A%2Acos%28+B%2At+%2B+C+%29+%2B+D+
+h%28t%29+=+-80%2Acos%28+B%2At+%2B+C+%29+%2B+85+
Two turns in 6 minutes is +%28+4%2Api+%29%2F6+=+%28+2%2Api+%29%2F3+
+B+=+%28+2%2Api+%29%2F3+
+C+=+0+ since there will be no phase shift
So now I have:
+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+
( checking this, when +t+=+6+, +B%2At+=+4%2Api+
which is 2 turns )
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(B)
+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+
+t+=+1+
+h%281%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29+%29+%2B+85+
+h%281%29+=+-80%2Acos%28+.667%2Api+%29+%2B+85+
+h%281%29+=+-80%2A%28-.5+%29+%2B+85+
+h%281%29+=+40+%2B+85+=+125+
At 1 min, her height is 125 ft
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This kind of makes sense, because at +t+=+1.5+,
The ferris wheel is at maximum height:
+h%28t%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2At+%29+%2B+85+
+h%281.5%29+=+-80%2Acos%28+%28+%28+2%2Api+%29%2F3%29%2A%283%2F2%29+%29+%2B+85+
+h%281.5%29+=+-80%2Acos%28+pi+%29+%2B+85+
+h%281.5%29+=+-80%2A%28-1%29+%2B+85+
+h%281.5%29+=+165+ ft
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Hope this helps -get other opinions if needed