Answer to Question #94850 in Trigonometry for may

Question

The third-tallest 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) = 67sin [12(t + 0.0223)] + 70.
a. What is the diameter of this Ferris wheel?

b. Where is the rider at t = 0? Explain the significance of this value.

c.How high off the ground is the rider at the top of the wheel?

d. At what time(s) will the rider be at the bottom of the Ferris wheel?

e.How long does it take for the Ferris wheel to go through one rotation?

Answer 1

a) Diameter of this Ferris wheel is double the amplitude $d=67\cdot 2=134m$

b)At t = 0 raider will be at height of $67sin [12(0 + 0.0223)] + 70=67sin(0.2676)+70\approx$ 87.71598.

c)Since $sin [12(t + 0.0223)] \leq1$ The rider is $67\cdot 1+70=137m$ high off the ground if he is at the top of the wheel.

d)Rider will be at the bottom of the Ferris wheel when his height is minimal, when $sin [12(t + 0.0223)] =-1, \ when\ 12(t + 0.0223)=3 \pi/4+2\pi\cdot k$

$(t + 0.0223)=(3 \pi/4+2\pi\cdot k)/12$

$t =- 0.0223+(3 \pi/4+2\pi\cdot k)/12=- 0.0223+\pi/16+\pi/6\cdot k$

e)If t₁ and t₂ are to consecutive moments when the rider is in the same place

$12(t_2 + 0.0223)-12(t_1 + 0.0223)=2\pi,\\ \ t_2-t_1=2\pi/12=\pi/6$

Answer: a) 134m, b)87.71598, c) 137m, d) $t =- 0.0223+\pi/16+\pi/6\cdot k$ e)$\pi/6$ .