anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
what's the direction of rotation?
anonymous
  • anonymous
clockwisei think. my teacher didnt specify but i think they usually go clockwise.
anonymous
  • anonymous
let y = A sin(kt + c) + h, where A is the amplitude, 2pi/k is the period, -c/k is the phase shift. There will be a phase shift since at t=0, the passengers are (1/8) of a rotation away from the bottom most point while moving downwards. A should be the radius of the ferris wheel, and k = 2pi/20, which reduces to pi/10. h is the distance above the ground plus the radius, so h = 11. I think the value of c should be -pi^2/40 since the phase shift is (-1/4)pi, so

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anonymous
  • anonymous
***sorry, thinking little more about the phase shift.
anonymous
  • anonymous
not entirely certain about the phase shift, but I think your equation should be y = 10sin((pi/10)t + pi^2/40) + 11

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