Question

The largest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67 sin[0.2094(t-30)] + 70.

a) At what time(s) will the rider be at the bottom of the Ferris wheel?
b) How long does it take for the Ferris wheel to go through one rotation?
c) What is the minimum value of this function? Explain the significance of this value.

Answer 1

The Ferris wheel will be at the bottom when \[\theta=3\pi/2\]
Part a:

Set \[3\pi/2=(.2094)t\]t=22.5 minutes or 22.5+(n)(30) where n is a positive integer.

Part b:

The Ferris wheel will make a complete rotation sweeping through \[2\pi\]

The angular speed is \[\omega=\theta/t\]\[\omega=.2094\]\[\theta=2\pi\]So the time will be \[2\pi/.2094=t\]

So t in minutes is\[t \approx30 \]

So it takes about 30 minutes for one rotation.

Part c:

The equation will be at a minimum when \[\omega t = 3\pi/2\] So the \[\sin 3\pi/2=-1\]

(67)(-1)+70=3 meters

This is the height of the bottom of the Ferris wheel to ground level.