One of the largest ferris wheel ever built is in the british airways london eye which was completed in 2000. The diameter is 135 m and passengers get on at the bottom 4 m above the ground. The wheel rotates once every three minutes.
a) Draw a graph which represents the height of a passenger in metres as a function of time in minutes.
b) Determine the equation that expresses your height h as a function of elapsed time t
c) How high is a passenger 5 minutes after the wheel starts rotating?
d) How many seconds after the wheel starts rotating is a passenger 85 m above the ground for the first time. Answer to the nearest tenth.
Please help me solve this equation and try and making to as clear as possible my solution lacks.
$\endgroup$ 72 Answers
$\begingroup$Your solution is on the right track. The question asks you to use time in minutes, so you should not convert to seconds. In that case $\omega=\frac {2\pi}3$ That changes your constant $45$ as well.
$\endgroup$ $\begingroup$This is a straightforward question and I strongly suggest that you go over your textbook or at least one of these following resources:
After that, try the problem again, checking against the answer below:
a)
b) $h(t) =\frac{135}{2} \sin(\frac{2 \pi}{3}x - \frac{\pi}{2}) + \frac{135}{2} + 4 = \frac{135}{2} \cos(\frac{2 \pi}{3}x + \pi) + \frac{135}{2} + 4$.
c) $h(5) = 105.25$ feet.
d) $h^{-1}(85) = 50.77 $ seconds.
Because you did not attempt to solve the problem yourself, I will not provide a detailed solution. If you run into trouble trying to complete the problem yourself, let me know in a comment and I may be able to help.
$\endgroup$
