math

A ferris wheel has radius of 25 m and its centre is 27 m above the ground. It rotates once every 40 seconds. Sandy gets on the ferris wheel at its lowest point and the wheel starts to rotate.

Determine a sinusodial equation that gives her height, h, above the ground as a function of the elapsed time, t, where h is in metres and t in seconds

all i know is that amplitude is 25
and period is 40
and the vertical displacement is 27

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  1. Such an equation is not unique, I thought

    h = 25sin π/20(t +30) + 27

    when t = 0 , h = 2 , let's say the platform to get on
    when t = 10 , h = 27 , that makes sense
    when t = 20, h = 52 , at the top, makes sense
    when t = 40, h = 2, back down to the start,

    looks ok

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  2. i don't get where the horizontal displacement of +30 comes from :S

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  3. I started with

    y = 25sin π/20(t) , sketch that graph

    I knew I had to raise it 27 metres

    but that the low point or the starting point of the ride at 30 seconds, we wanted that to be at 0 seconds, so I had to move the whole curve 30 seconds to the left.

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