Question 1031226: A Ferris wheel has a radius of 75 feet. You board a car at
the bottom of the Ferris wheel, which is 10 feet above the ground, and rotate
2558 counterclockwise before the ride temporarily stops. How high above
the ground are you when the ride stops? If the radius of the Ferris wheel is
doubled, is your height above the ground doubled? Explain.
Thanks a million for the help. I am stuck.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw this. Radius is 75 feet.
Circumference is 2*pi*r=471.24 feet
5 times around is 5*471.24=2356.19 feet
You are 2558-2356 feet into the fourth revolution, or 201.80 feet
That is 0.428 way around the circle or 154.16 degrees from the bottom.
The 3 o'clock position is the x-axis and it is 117.81 feet from the bottom, so the seat is 83.99 feet above that on the circle.
83.99/75 is 1.12 radians.
The sine of the angle made by the seat to the center to the x-axis is the sine of 1.12 radians divided by 75, the radius (and the hypotenuse of the triangle). It is 0.9001.That is 64.17 degrees. Note, once we know the number of degrees from the bottom, we know the angle, because 90 takes us to the x-axis. This is a check.
The sine is also the height above the x-axis divided by the hypotenuse. It is 67.5075 or 67.5 feet. Therefore, the seat is 10+75+67.5 feet off the ground or 152.5 feet
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If the radius is doubled, the height is almost doubled, but not quite, because the 10 feet you are off the ground has not changed.
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