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Math Help - Height of Ferris Wheel at t=0

  1. #1
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    Height of Ferris Wheel at t=0

    The largest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67 sin[0.2094(t-30)] + 70.

    Where is the rider at t = 0? Explain the significance of this
    value.

    This is what I've done:

    h(t) = 67 sin[0.2094(t-30)] + 70
    h(0) = 67 sin[0.2094(0-30)] + 70
    h(0) = 67 sin[0.2094(-30)] + 70
    h(0) = 67 sin(-6.282) + 70
    h(0) = -7.331276925 + 70
    h(0) = 62.67 m

    Therefore, the rider would be at 62.67m at zero seconds which would mean that he or she would be 62.67m above the ground when they started the ride. However, that doesn't make sense because the rider should be starting the ride at the bottom.

    I would think the starting point of the ride would be -1(67) + 70 = 3m.

    Please help!
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  2. #2
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    Re: Height of Ferris Wheel at t=0

    Quote Originally Posted by starshine84 View Post
    The largest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67 sin[0.2094(t-30)] + 70.

    Where is the rider at t = 0? Explain the significance of this
    value.

    This is what I've done:

    h(t) = 67 sin[0.2094(t-30)] + 70
    h(0) = 67 sin[0.2094(0-30)] + 70
    h(0) = 67 sin[0.2094(-30)] + 70
    h(0) = 67 sin(-6.282) + 70
    h(0) = -7.331276925 + 70
    h(0) = 62.67 m

    Therefore, the rider would be at 62.67m at zero seconds which would mean that he or she would be 62.67m above the ground when they started the ride. However, that doesn't make sense because the rider should be starting the ride at the bottom.

    I would think the starting point of the ride would be -1(67) + 70 = 3m.

    Please help!
    A couple of comments here. Practically speaking a Ferris Wheel loads its passengers from the bottom, but increments the passengers around the ride as others are loaded. The ride starts, then, when all passengers are loaded, which can mean that you are up in the air when the ride starts.

    My second comment is to make sure that you should be using the degree mode on your calculator. Most (but not all) problems like this use radians.

    -Dan
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  3. #3
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    Re: Height of Ferris Wheel at t=0

    My entire course has used degrees so I assume it is the same for this problem. My calculator is in degree more.

    For the starting point of the ride, I suppose you could be right... they could be starting the ride from the halfway point, it just seems very strange, particularly because the London Eye never actually stops moving even to load passengers.
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  4. #4
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    Re: Height of Ferris Wheel at t=0

    Quote Originally Posted by starshine84 View Post
    The largest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67 sin[0.2094(t-30)] + 70.

    Where is the rider at t = 0? Explain the significance of this
    value.

    This is what I've done:

    h(t) = 67 sin[0.2094(t-30)] + 70
    h(0) = 67 sin[0.2094(0-30)] + 70
    h(0) = 67 sin[0.2094(-30)] + 70
    h(0) = 67 sin(-6.282) + 70
    h(0) = -7.331276925 + 70
    h(0) = 62.67 m

    Therefore, the rider would be at 62.67m at zero seconds which would mean that he or she would be 62.67m above the ground when they started the ride. However, that doesn't make sense because the rider should be starting the ride at the bottom.

    I would think the starting point of the ride would be -1(67) + 70 = 3m.

    Please help!
    I suspect that the factor 0.2094 \approx \dfrac{2\pi}{30}

    If so:
    1. you have to use your calculator in radians mode.

    2. h(0)=67 \cdot \sin(-2\pi)+70=70

    But according to your last post you don't use radians mode ...
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  5. #5
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    Re: Height of Ferris Wheel at t=0

    I think I have it figured out now, thanks for your help
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