Find an Online Tutor Now

Aarabi M.

asked • 08/23/17

trigonometry question?

Kevin is riding a mini Ferris wheel. He reaches the maximum height of 9m at 5s and then reaches the minimum height of 1m at 65s.
a.What is the period (the length of time to complete one cycle)?
b.what is the radius of the wheel?
c.sketch one cycle of the function. Label the graph.
d.the corresponding cosine equation:

1 Expert Answer

By:

Arturo O. answered • 08/23/17

Tutor
5.0 (66)

Experienced Physics Teacher for Physics Tutoring

See tutors like this
See tutors like this
(a)
 
He completes 1 cycle in twice the time it takes to complete half a cycle.  It takes half a cycle to get from the top to the bottom.
 
T = 2(65 - 5) s = 120 s
 
(b)
 
The difference between maximum and minimum heights must equal twice the radius.
 
2r = (9 - 1) m
 
r = 4 m
 
(c)
 
Unable to graph or sketch in this format.
 
(d)
 
I am not clear what you mean by "corresponding cosine equation".
Upvote • 0 Downvote
More
Report

Arturo O.

Perhaps you meant to find an equation for height as a function of time, using the cosine function?  If so, then
 
h(t) = hmin + r + r cos[ω(t - 5)] = 1 + 4{1 + cos[ω(t - 5)]}
 
h(t) = 1 + 4{1 + cos[ω(t - 5)]},
 
where
 
cos[ω(t - 5)] is the angle measured from the upward vertical radius of the wheel.  The (t - 5) in the  cosine accounts for a head start of 5 seconds at the top.
 
ω = 2π/T = 2π/120 rad/sec = π/60 rad/sec
 
h(t) = 1 + 4{1 + cos[(π/60)(t - 5)]},
 
with t in seconds, the angle in radians, and h in meters.  Test it.
 
Is h(5) = 9 ?
 
h(5) = 1 + 4{1 + cos[(π/60)(5 - 5)]} = 1 + 4(1 + cos0) = 1 + 4(1 + 1) = 9  [good]
 
Is h(65) = 1 ?
 
h(65) = 1 + 4{1 + cos[(π/60)(65 - 5)]} = 1 + 4(1 + cosπ) = 1 + 4(1 -1) = 1  [good]
Report

08/23/17

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.