Jack O.

asked • 03/01/18# Determine the height of a capsule/pod above the ground after 25 mins.

The diameter of the "Eye" is 135 meters and each rotation takes 30 mins. By first developing a suitable model to represent the rotation of the "Eye", determine the height of a capsule/pod above the ground after 25 minutes.

The London Eye is a major tourist attraction in London, England. During a ride on the "Eye", the rotation can be modeled using a periodic function.

State any assumptions made in determining your results.

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## 1 Expert Answer

Michael P. answered • 03/01/18

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This is difficult to explain without a drawing.

Let d = diameter of the Eye = 135 m

r = radius of the Eye = d/2 = 67.5 m

t = 25 min

assume ho = 1 meter above ground for loading at initial theta = 0; or &theta = -90

^{o}1 rev = 360

^{o}/30 min = 12^{o}/minθ = (12

^{o}/min)*t h = ho + r*(1 + sin(θ

^{o}+ θ)) General Solutionat t = 25 min

h = 1 m + (67.5)*[1 + sin(-90+ 12*(25) ] = 34.75 m above ground after 25 min

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Michael P.

03/01/18