A Ferris wheel has a radius of 31.6 feet. The bottom of the Ferris wheel sits 0.

Question

A Ferris wheel has a radius of 31.6 feet. The bottom of the Ferris wheel sits 0.6 feet above the ground. You board the Ferris wheel at the 3 o'clock position and rotate counter-clockwise. Define a function, f that gives your height above the ground (in feet) in terms of the angle of rotation (measured in radians) you have swept out from the 3 o'clock position, a. Define a function, g, that gives your height above the ground (in feet) in terms of the number of feet you have rotated counter-clockwise from the 3 o'clock position, s

Explanation / Answer

It is trigonometric function

f(a) = 0.6 +31.6 +31.6sin(a ) where a is the angle rotated anticlockwise

at a = pi/2 when the freeis whell is on top; f(a) = 32.2 +31.6sin(pi/2) = 63.8

So, it is verfied

f(a) = 32.2 +31.6sin(pi/2)

arc length = s ; radius = 31.6

Ange rotated = s/r = s/31.6

So, f(s) = 32.2 +31.6sin(s/31.6)

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