Math (Trig)

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a ferris wheel has a radius of 10m and is one meter above the ground. If the ferris wheel makes 1 revolution every 20 seconds, write an equation that gives the height above the ground of a person on the ferris wheel as a function of time if that person starts (t=0) 1/8th of a rotation away from the bottom most point while moving downwards

please help!!

  • Math (Trig) -

    1 rotation = 2pi
    1/8 rotation = 1/8 x 2pi = pi/4

    State y as the height difference created from the rotation of the wheel and the bottom of the ferris wheel (not the ground)
    height = y + 1
    = r - r cos {(2pi/20)t - (pi/4)} +1
    = r(1 - cos pi{(t/10) - (1/4)}) +1
    = 10(1 - cos pi{(t/10) - (1/4)}) +1

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