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# geometry problem

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Riders on a Ferris wheel travel in a circle in a vertical plane.  A particular wheel has radius 20 feet and revolves at the constant rate of one revolution per minute.  How many seconds does it take a rider to travel from the bottom of the wheel to a point 20 vertical feet above the bottom?

Feb 13, 2021

#1
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10 seconds

Feb 13, 2021
#2
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In one minutes, the wheel has spun once, so it has traveled \(40pi\) feet.
So we have: 60 sec. = 40 pi feet, so ? sec. = 20 feet.

So ? = 60/2pi = 30/pi sec.

30/3pi is about 9.55. So to the nearest integer, the answer is 10.

Feb 13, 2021
#3
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30/pi not 30/3pi, sorry.

Guest Feb 13, 2021
#4
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If  we  imagine  a circle  with an equation  of  x^2   + y^2 =   20^2

The   coordinates  at the   bottom of the wheel =  (0, -20)

When the wheel  is  20 vertical feet  from  the  bottom (assuming a  counter-clockwise rotation)  it is at  (20, 0)

This position represents  a  1/4  turn of the  wheel ......so....it must take the  wheel  (1/4) (60)   =15  seconds to  reach  this point

Feb 13, 2021