Question 878797: This question is a homework question but I think that the formula is wrong. I could be wrong though. I need someone to PLEASE work me through this because I honestly have no clue what to do.
Travis is riding the Ferris wheel at the amusement park. His height can be modeled by the equation
H(t) = 22 cos (pi over 13)t + 28, where H represents the height of the person above the ground in feet at t seconds.
Part 1: How far above the ground is Travis before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Travis begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Travis' height above the ground reaches a minimum?
part 1 I believe is 28. Part 2 doesn't make sense to me. since t is outside of the parenthesis, wouldn't it take forever to make a full rotation? I don't think the formula is correct. For part three, would it be 13? I am saying that because of the 13 that appears in the equation. Although I think I am wrong. I am never any good with trigonometry or formulas. I need some help with this pretty please! I would really appreciate it!!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Travis is riding the Ferris wheel at the amusement park. His height can be modeled by the equation
H(t) = 22 cos (pi over 13)t + 28, where H represents the height of the person above the ground in feet at t seconds.
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Given equation follows the form: y=Acos(Bx-C)+D, A=amplitude, period=2π/B, C/B=phase shift, D=vertical shift
..
For given equation: H(t) = 22 cos (pi over 13)t + 28
amplitude=22
B=π/13
period=2π/B=2π/(π/13)=26 sec
Phase shift=0
vertical shift=28
...
Part 1: How far above the ground is Travis before the ride begins?
H(0) = 22 cos (pi over 13)*0 + 28=22+58=50 ft
H(0) = 22 cos (0) + 28=22+58=50 ft
..
Part 2: How long does the Ferris wheel take to make one complete revolution?
period=2π/B=2π/(π/13)=26 sec
..
Part 3: Assuming Travis begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Travis' height above the ground reaches a minimum?
Cos function reaches a minimum at 1/2 period=13 sec
H(13)=22cos(π/13*13)+vertical shift of 28 up
H(13)=22cos(π)+vertical shift of 28
H(13)=22*(-1)+ 28=-22+28=6 ft
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