How long does it take the ferris wheel to make one full rotation?

h(t)=9sin(20(t-pi/2))+12 , h in metres and t in seconds

Question

21-07-2014
Mathematics

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How long does it take the ferris wheel to make one full rotation?

h(t)=9sin(20(t-pi/2))+12 , h in metres and t in seconds

Sagot :

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AL2006 AL2006 · Answer 1 · 2014-07-21T20:52:20-04:00

This is a circular ferris wheel, with diameter of 9 meters, and the axis
mounted 12 meters off the ground. The equation is the height of the
a point that starts out level with the axis, at 't' seconds after the wheel
starts up.

Now here's where things start to go awry:

The period of the revolution is the time it takes for the angle
inside the sine to change by 2pi .

20(t - pi/2) = 2pi

20t - 10pi = 2pi

20t = 12pi

t = 12pi/20 = 1.885 seconds

I can't help it. All I did was the math, and that was bullet-proof.
It was up to whoever wrote the question to guarantee that the
answer makes sense.

For one thing, I don't believe the 'pi/2' belongs inside the parentheses
with the 't'. But even if we take the 'pi/2' out of the parentheses, that
still only makes the period 3.183 seconds, which is still an uncomfortable
number ... especially for the riders.

Sagot :

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