Question

1.Jim and Chana are riding the Ferris wheel like the one diagrammed here. It is supported on a triangular base having a bottom of 18.460m and sides of 14.359m. During the ride Jim observed Chana, while Chana observed that at the bottom of the ride she passed the two structural supports 8 seconds apart. If the Ferris wheel is elevated 1m off the ground, create an equation to model Jim and Chana’s height as they ride the wheel (the ride starts at the bottom). Show all calculations and describe how you determined each of the factors in the final equation. Round any angle calculation results to the nearest degree.

Answer 1

Clearly, the radius of the wheel is 9.98, or, due to the careful engineering of the triangle, call it 10 meters.

So, the height, starting at the bottom, will be

h = 11-10cos(kt)

So, we just need to find k. The vertex angle of the triangle satisfies

sin θ/2 = 9.23/14.35
so, θ = 80°

Thus, the wheel turns 2/9 of a circle in 8 seconds, giving it a period of 36 seconds. Our function is thus

h = 11-10cos(π/18 t)

Answer 2

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